| How to Find the Equation of a Line Posted: 17 Jan 2020 12:00 AM PST Finding the equation for a line is a common problem in geometry and trigonometry. There are two common situations where you are asked to find the equation for a line: either you'll be provided with one point on the line and the slope of the line, or you'll be provided two points on the line. In either case, finding the equation for that line isn't difficult, provided you use the correct formula and work carefully. [Edit]Calculating the Equation with One Point and the Slope - Plug the slope in for m in the formula y-y1 = m(x-x1). This is known as the point-slope formula. The point-slope formula uses the slope and the coordinates of a point along the line to find the y-intercept. Use the slope in place of m in y-y1 = m(x-x1).[1]
- For example, if you know the slope of the line is 2, then your formula will look like this: y-y1 = 2(x-x1).
- Replace x1 and y1 with the coordinates of the point. Use the coordinates you're given as (x1, y1). Put the numbers in the corresponding spot on your formula before you start solving the equation.[2]
- Solve the formula for y to get the final slope-intercept formula. Follow the mathematical order of operations and the distributive property to remove the x-term from parenthesis.
- In our example, first you'd use the distributive property to get y-3=2x-8.
- Then, add 3 to each side so y is by itself.
- The final equation for a line in slope-intercept form with a slope of 2 that contains the point (4, 3) is y = 2x-5.
[Edit]Finding the Equation Using Two Points - Find the slope using m = (y2-y1)/(x2-x1). The ordered pairs of the coordinates you have are listed as (x, y). Use the first set of coordinates as (x1, y1) and the second set as (x2, y2). Plug the numbers into the formula m = (y2-y1)/(x2-x1) and solve for m.[3]
- Replace the m in the slope-intercept formula with the slope you found. The slope-intercept formula of a line is written as y = mx+b, where m is the slope and b is the y-intercept (the point on the y-axis where the line crosses it). Plug the number you found for your slope in place of m.[4]
- In our example, the formula would read y = 1x+b or y = x+b when you replace the slope value.
- Substitute x and y for one of the points you know to solve for the y-intercept. Pick one of the ordered pairs to put into the slope-intercept formula. Put the x-value in place of x and the y-value in place of y.[5]
- In this example, if you chose (3, 8) as your coordinates, then the formula would read 8 = 1(3)+b.
- Solve the equation for b. Once you plug the x- and y-values as well as your slope into the formula, find the value of b in the equation. Follow the order of operations first before moving the rest of the numbers to the other side. Leave b on one side of the equation to solve it.[6]
- In our example, the formula currently reads 8 = 1(3)+b. Multiply 1 and 3 together to get 8 = 3+b. Since 3 is a positive number, subtract 3 from each side to isolate b. This leaves you with 5 = b, or b = 5.
- Plug in the slope and y-intercept into the slope-intercept formula to finish the equation. Once you're finished, plug in the slope for m and the y-intercept for b. After that, you've found the equation for the line.
- For example, the equation for the line with points on (3, 8) and (7, 12) is y = 1x+5 or simply y = x+5.
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| How to Make Rose Petal Perfume Posted: 16 Jan 2020 04:00 PM PST Floral perfumes and fragrances are perfect for making yourself smell like a summer garden. However, you don't need to spend a lot of money to make that happen! With just a few ingredients, you can create your own perfume to use for yourself or give as a gift to someone else. [Edit]Ingredients [Edit]Alcohol-Based Perfume - 3/4 cup (180 g) of fresh rose petals
- of vodka (80-100 proof)
- of distilled water
[Edit]Scented Rosewater - 1/2 cup (120 g) of fresh rose petals
- of distilled water
[Edit]Creating an Alcohol-Based Perfume - Rinse the roses gently in cold water. If the water is too warm, it may release some of the flower's aromatic oils before you collect them. Rinsing will remove fertilizer, dirt, insects, and any other contaminants you don't want inside your perfume. Don't worry about trying to rinse thoroughly between the petals.[1]
- Do not dry the petals after rinsing.
- Depending on the type of rose and the size of the petals, you will probably need between 1 and 3 roses.
- Remove of petals from the roses. Note that the petals can come from any type or color of rose. To remove the petals, grasp the stem with one hand and tear the petals off with the other. Be careful not to skewer yourself on any thorns.[2]
- Consider using a thorn stripper if you're very concerned with pricking yourself on the thorns.
- Place the petals in a large glass jar with a lid. You can also use a bowl if it comes with a lid too, but whatever option you choose must be able to hold at least of liquid and be sealable. A mason jar with a screw-top lid would work well.
- Pour of vodka into the jar to soak for 24 hours. Vodka that is 40-50 percent alcohol (80-100 proof) works best. The jar should also be stored someplace that is cool and dark, like a cabinet or cupboard. Do not use a fridge, which is damp.[3]
- Pulverize the petals for 45 seconds with a spoon. A large wooden cooking spoon would work best for mashing the petals inside the jar. A mortar and pestle might cause you to lose some of the rose oils by removing the petals from the jar, and a metal spoon could add unwanted metallic elements to the perfume.
- Add of distilled water to the jar. Distilled water can be purchased at most grocery stores or drug stores. The more water you add, the more diluted the scent of the perfume will be.[4]
- Cover the jar and place it in a cool, dark location for 4-7 days. Once a day, stir the petals and mash them again with a cooking spoon. Do not add more distilled water. Replace the lid quickly after you stir.
- Strain the mixture into clean glass perfume bottles. Use a fine mesh strainer to remove the spent petals from the liquid and transfer the liquid to a glass bottle with a tight lid. To best preserve the perfume, keep it in the fridge and shake it before each use. It will last up to a month. The scent will be strongest if you spray it on the warmer places of your body like your wrist and neck.[5]
- You could also use a sieve or a cheesecloth for straining.
[Edit]Making Scented Rosewater - Collect of rose petals in a medium-sized bowl. Any variety of rose will do. If you'd like, rinse the petals in cold water beforehand to wash away any contaminants that might still be on the flower. Be careful not to prick yourself on any thorns.[6]
- Stir in of warmed distilled water into the bowl of petals. The water's warmth will help increase the oil output from the rose. If you'd like, let the water soak in for about five minutes. The longer you let the petals soak, the stronger the fragrance will be.[7]
- Pour the mixture into a strainer placed over a second bowl. If you don't have a normal kitchen strainer, you can also use a cheesecloth. Do not throw the water that you separate away, as you will be reusing it in subsequent steps.[8]
- The rose petals should remain behind in the strainer, and the water should be in the second bowl.
- Grind the petals with a mortar and pestle. To remove the petals from the strainer, scrape them off with a spoon or pick them off with your fingers. If you don't want to grind the petals, don't strain them to begin with. Instead, let them sit in the distilled water under the sun for 5-7 hours.[9]
- Letting the petals soak in the sun does mean that the eventual fragrance will be much weaker.
- Add the water from the second bowl back to the petals. Let the water soak into the petals again for at least five minutes. By this point, the ground up petals with the added water should be in the first bowl.
- Repeat the straining, grinding process until the water is brownish-orange. If you are using dark colored rose petals like deep red, the water will turn brownish-red instead. Try not to grind the petals too violently, as any water you splatter is water that won't end up as perfume.[10]
- Strain out the petals and squeeze out any remaining water from them. A spoon might be effective for this. Then, pour the water into an empty perfume bottle using a small funnel and enjoy! Refrigerate to make the perfume last longer.[11]
[Edit]Warnings - Keep away from sensitive skin and your eyes, nose, and mouth.
[Edit]Things You'll Need [Edit]Alcohol-Based Perfume - Large glass jar or bowl with lid
- Large wooden cooking spoon
- 1-2 small empty glass perfume bottles
- Kitchen strainer or cheesecloth
[Edit]Scented Rosewater - 2 medium-sized bowls
- Mortar and pestle
- Kitchen strainer or cheesecloth
- 1-2 small empty glass perfume bottles
- Small funnel with spout
- Spoon (optional)
[Edit]Related wikiHows [Edit]References |
| How to Drive Long Distances Alone Posted: 16 Jan 2020 08:00 AM PST If you're feeling anxious about taking a big trip alone, look at the drive as an opportunity to enjoy some time to yourself. As long as you plan for traveling and prepare for emergencies, you should safely manage the drive. Pack snacks, dress comfortably, and bring your favorite music. Then, relax and enjoy the solitude as you put the miles behind you. [Edit]Getting Ready for a Trip - Plan your route and include stopping points. Decide which main roads you'll take to get to your destination and pick any places of interest you want to see along the way. Even if you're trying to drive straight to your destination, make notes of rest stops along the route. It's important to plan even if you'll be using your GPS since you might lose the signal or run out of battery.[1]
- If you're driving for several days, make an itinerary for how far you want to drive each day. For example, you might want to drive 7 hours for the first day, but only drive 5 hours the next.
- Pack your car with everything you need for the trip. In addition to your luggage, bring a little cash along with your credit cards. Remember to have your license and proof of car insurance in your vehicle. It's also a good idea to pack physical maps even if you'll be relying on your car or phone's GPS.[2]
- If you're crossing borders, check that your passport is still valid and pack it in a safe place in the car.
- Don't forget your phone charger, especially if you're using the phone a lot to navigate.
- Schedule a car inspection before your trip. In the week before you travel, get your car looked at by a mechanic and ask them if there are any issues to fix. Getting your car in shape could prevent mechanical emergencies during your trip. You might need to get an oil change, top up the fluids, replace an air filter, or get new tires, for instance.[3]
- Do this well before your trip so you can schedule additional maintenance as needed.
- Load the car with emergency car supplies. No one wants to experience a flat tire or road emergency, but it's best to be prepared. Pack a spare tire along with any other supplies you might need. For example, if you're traveling through a hot location and worry that your car might overheat, pack a jug of water or coolant. Consider traveling with:[4]
- Jumper cables
- Flashlights
- First aid kit
- Simple tool kit
- Blanket or sleeping bag
- Inform family and friends about your plans. Since you'll be traveling alone, it's important to let people close to you know where you'll be. Tell them your route, let them know when you'll be passing through each destination, and tell them you'll contact them along the way.[5]
- Email the info or write it down so your family or friends can refer back to the information.
[Edit]Making the Drive Enjoyable - Wear comfortable clothes so you feel relaxed. Avoid dressing in tight, restrictive clothing since you'll be sitting for a long time. Choose light, loose fabrics that allow you to move easily. Layer your clothes so you can stay warm or cool during your drive.[6]
- If you start driving in the morning when it's cool, you might want a fleece jacket. You can remove it later when you warm up or drive to a hotter destination.
- Listen to your favorite music. Load an MP3 player with a variety of your favorite music or pack plenty of CDs. Enjoying music is a great way to pass the time during a long drive.[7]
- If you don't like listening to music in the car, find an audiobook or podcast to enjoy.
- Pack healthy snacks to munch on. Keep easy-to-eat snacks in the passenger seat so you can eat something when you feel hungry. Snacking on something healthy is also a good way to stay awake since it will help you focus on something. Avoid snacking on salty foods, which can dehydrate you. Good snack options include:[8]
- Granola bars
- Unsalted nuts
- Rice cakes
- Fresh fruit and vegetables
- Crackers
- Bring refreshing beverages to drink so you stay hydrated. Water is one of the best drinks for a long car ride, but you could also bring coffee, tea, caffeinated drinks, or juice. Avoid drinks with a lot of added sugar, such as energy drinks, which could make you jittery.[9]
- If you'd like the drinks to stay cool, put them into a small cooler and place it near the bottom of the passenger street so it's easy to get to.
- Don't look at the clock to track how far you've driven. If you're in a hurry to get to your destination, glancing at the clock every few minutes will only make you more stressed. Make a point of not looking at the clock. Instead, relax and try to enjoy the drive.[10]
- Instead of focusing on how much longer you have in the car, think about how many miles you've put behind you.
[Edit]Staying Safe While Driving Alone - Take a popular route with major roads. Stick to your travel itinerary and avoid taking shortcuts. If you do need to take a detour, follow the detour signs closely. Don't take unmarked roads or routes that you're unsure of.[11]
- Stay on main roads so you can stop and ask for help if necessary.
- Adjust your travel plans if the weather worsens and you don't feel comfortable driving.
- Follow the local traffic laws and drive below the speed limit. Always wear your seat belt and be aware of your surroundings. Avoid speeding or breaking local traffic laws. Instead, drive cautiously and safely.[12]
- If you're driving into a foreign country, it's especially important to read about their driving laws since they might be very different than the ones you're used to.
- Pull off and take a short nap if you feel drowsy. Find a safe, well-lit location and park your car. Lock your doors and close your eyes for 20 to 30 minutes. It's better to take a little time to rest than risk getting into an accident by driving drowsy.[13]
- Start your journey after a good night's sleep so you're less likely to be tired on the drive.
- Drink something caffeinated before you rest so you wake up feeling more energized.
- Avoid talking on the phone or texting while you drive. It's illegal to talk on a cell phone or text in many areas, so don't use your phone or you may get a ticket. Talking on the phone or texting distracts you when you should be focusing on your surroundings.[14]
- If you do need to take a call, pull off to a safe spot and have your conversation.
- Having a hands-free phone call is just as distracting as holding the phone up to your ear, so avoid using a headset to call someone.
- Take rest breaks to recharge. Getting out of the car for a few minutes to stretch your legs and use the restroom is a simple way to break up the drive. You can use these short breaks to contact friends or family and tell them where you're at.[15]
- Stop at designated rest stops or well-lit businesses. Avoid taking a break on the side of the road or in an unsafe area.
- Pay attention to signs that show how far away the next service station is and don't wait until your gas tank is on empty before refueling.
- Carry a gasoline container with a gallon of gasoline, in case your car runs out before you are able to reach a service station. Make sure you read all the instructions on the canister and store it safely.
- Keep your mind engaged by playing the alphabet game. Repeat the alphabet by taking one letter from each sign, billboard, advertising on trucks, or license plate.
[Edit]Warnings - Remember that each state and country has different laws. If you're traveling across borders, do some research about the local rules of the road.
- Don't share personal details about yourself or your travel plans to strangers.
[Edit]Related wikiHows [Edit]References |
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