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 ([tex]y_{2}-y_{1}[/tex]) over the change in x, looking like [tex] \frac{y_{2}-y_{1}}{ x_{2}- x_{1} }[/tex]. 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
[tex] \frac{y_{1}-y_{2}}{ x_{1}- x_{2} }[/tex]. 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
[tex] \frac{48-28}{ 10-5 }= \frac{20}{5} =4[/tex] 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!
