The nature club is renting vans. the vans costs $6 per student. The van company also charges a $24 service fee per van. The club can spend $168

Question

Linear graph by using an equation

Answer 1

Hi Steph!! 

So first thing when writing a linear equation is figuring out which variable is the independent variable, x, and the dependent variable, y. In this situation the cost depends on the number of students so the cost is y and the number of students is x. We know this relationship is linear so we can use slope intercept form, y=mx+b, where m is the slope and b is the y intercept. So now where to the values you are given go. This is the more challenging part. The best thing to do here is think logically first and then try to apply math to find your answer. We know if they charge $6 per student then that would be 6x for the cost. Then we have to think about where the $24 would come in. This charge is should be added in to the student cost. so now we have 6x + 24. This is the total cost the nature club is paying for the van so 6x+24=y. This is the linear function that represents this situation. So we have one piece of information that we haven't used yet, the $168. This is how much the nature club can spend. So you can plug 168 in for y in the equation and solve for x to find the number of students they can take on the trip. Remember when you are solving to get x by itself by undoing what is being done in the equation, what you do on one side you must do on the other to keep the equation balanced. Hope this helps!! :)