Problem: Article: Determine whether the two variables are directly proportional: xy=6{\displaystyle xy=6}. Remember that if the variables are directly proportional, they will follow the pattern y=kx{\displaystyle y=kx}. Use algebra to rewrite the equation. Isolate the y{\displaystyle y} variable by dividing each side by x{\displaystyle x}:xyx=6x{\displaystyle {
rac {xy}{x}}={
rac {6}{x}}}y=61x{\displaystyle y=6{
rac {1}{x}}} Assess whether the rewritten equation follows the pattern y=kx{\displaystyle y=kx}. In this instance, the equation does not, so the variables are not directly proportional. In fact, they are inversely proportional. Are the variables directly proportional?xy1339927{\displaystyle {egin{matrix}x&y\\hline \1&3\3&9\9&27\end{matrix}}} Determine the growth of x{\displaystyle x}. Do this by finding the factor you multiply the first x-coordinate by to reach the second coordinate:1k=3{\displaystyle 1k=3}1k1=31{\displaystyle {
rac {1k}{1}}={
rac {3}{1}}}k=3{\displaystyle k=3}So, the x-coordinate grows by factor of 3. Determine the growth of y{\displaystyle y}:3k=9{\displaystyle 3k=9}3k3=93{\displaystyle {
rac {3k}{3}}={
rac {9}{3}}}k=3{\displaystyle k=3}So, the y-coordinate grows by factor of 3. Compare the factor, or constant, of the two variables. They both grow by a factor of 3. Therefore, the variables are directly proportional. Does the graph show direct proportion between variables? Note whether the line is straight. Since the equation of the line is in slope-intercept form, it has a constant slope, meaning the line is straight. So potentially, the variables are directly proportional. Determine the y-intercept. If the variables are directly proportional, the line will pass through the point (0,0){\displaystyle (0,0)}. The y-intercept of this line is the point (0,3){\displaystyle (0,3)}. So, the variables are not directly proportional.
Summary: Look at the equation. Consider the following set of points. Consider a graph of the line y=4x+3{\displaystyle y=4x+3}.

INPUT ARTICLE: Article: You can find companies in a phone book or online that allow you to rent a skid steer. Make sure that the company you choose will provide an experienced operator if you don't know how to use a skid steer yourself. Explain that you need to move large rocks and make an appointment for the skid steer and operator to meet you where the rocks are located. A skid steer is a multipurpose vehicle, like a Bobcat, that can be used to move heavy objects. It typically costs around $175 to rent a skid steer for 4 hours, plus the labor rate of around $50 per hour for the operator. Generally, a skid steer with a bucket or forks will be used for moving large rocks. Point out the rocks you need moved to the operator so they can load them into the bucket or onto the forks. The operator will place the forks or bucket underneath the rocks and lift them up. Make sure the path is clear for the skid steer to move from 1 location to the next. Once you've got the skid steer in the right location, ask the operator to unload the rocks. They will lower the forks or bucket and deposit the rocks on the ground.

SUMMARY: Arrange to have a skid steer and operator come to the location. Load the rocks in the skid steer. Drive the skid steer to the desired location and unload it.

In one sentence, describe what the following article is about: Sometimes the dentist is able to reattach the portion of tooth that broke off, so you should save it if you can. Take the shard and put it in a container with milk or saliva to keep it from rotting. Then bring it with you when you visit the dentist. You should never try to reattach the portion of tooth yourself. Not only will this not work without proper equipment, but you'll cause severe pain for yourself if you poke an exposed nerve. Your mouth is full of bacteria, and any injuries can get infected easily. To help stave off infection, rinse your mouth with a salt water solution when you know you've broken a tooth. Mix 1 tsp of salt into 1 cup of warm water. Swish the mixture around your mouth for 30 to 60 seconds.Concentrate on the injured area. Be sure not to swallow any of the mixture. Repeat this rinse after meals. If you've damaged your tooth badly, the pain can be severe. You can treat it with OTC pain relievers until you go to the dentist and get it fixed. Ibuprofen products like Motrin and Advil are usually preferred over acetaminophen because ibuprofen also reduces swelling in addition to treating pain. But if ibuprofen isn't available, take an acetaminophen product like Tylenol. Sometimes a chip in the tooth will produce a jagged edge that could cut your tongue or gums. To prevent damage to your mouth, cover the edge with dental wax. You an purchase this in the oral care aisle of most pharmacies. Alternatively, you could also cover the edge with a piece of sugar-free chewing gum. It's possible that you won't be able to see your dentist for several days after you crack your tooth. In this case, you'll have to eat before your appointment. Take the following measures to reduce pain and prevent further damage when eating. Stick with soft foods. The cracked tooth is weakened and susceptible to further damage. Hard foods could make the crack worse and cause pain. Opt for soft foods like pudding, soup, and oatmeal until your doctor performs the necessary work. Don't eat anything especially hot or cold. The cracked tooth will be sensitive to extreme temperatures, and very cold or hot foods can cause pain. Serve food at room temperature to avoid any problems. Try to eat on the unaffected side of your mouth. Any chewing can cause pain and further damage, so if possible you should avoid chewing with the cracked tooth.
Summary:
Save the shard of tooth if you have it. Rinse your mouth with salt water. Take over the counter pain relievers to help with the pain. Cover sharp edges with dental wax. Be careful when eating until you see your dentist.