Question

• Using the information in the table above, write the linear equation that represents the cost, (y) of buying different amounts of books, (x).

• How much would it cost for 30 books?

• How many books would you get for $160?

Answer 1

Alright, so one way to show the equation of a linear line is y=mx+b, where m is the slope. To find the slope of a line when you have multiple points, find the change in y (
`y_(2)-y_(1)`) over the change in x, looking like
`(y_(2)-y_(1))/( x_(2)- x_(1) )`. You can switch the 2 and the 1 in the y values as long as you switch it in the x ones as well, or make the equation

`(y_(1)-y_(2))/( x_(1)- x_(2) )`. Next, we want to plug in some coordinates - we have 5 as the x value and 28 as the y value, or (5,28) as one point. Next, we have (10,48) as another. Using the formula and plugging numbers in, we get

`(48-28)/( 10-5 )= (20)/(5) =4` as our slope. In the formula y=mx+b, that means that m=4 and our equation is y=4x+b. To find b, we have to plug in a point, such as (5,28). Using that, we get 28=5*4+b. Subtracting 5*4=20 from both sides of the equation, we get b=8 and our equation to be y=4x+8.

Since the books are the x value, that means that we can plug 30 in for x as there are 30 books to get the cost, or y, to be 30*4+8=120+8=128.

Since the cost is the y value, we plug 160 in for y to get 160=4x+8. Subtracting 8 from both sides, we get 152=4x. Next, dividing both sides by 4, we get 38=x, or the amount of books you can get with 160$.

Feel free to ask further questions!