# Solving Linear Relations

Once you have an equation to describe a linear relation, you can use it to solve for other terms. To solve for the y value, substitute the value for x and solve. To solve for the x value, substitute the value for y and isolate to get x.

Consider the following relationship between the number of toppings on a pizza and the cost:

 # Toppings Cost ($) 0 1 2 3 10 11.5 13 14.5 Since I love toppings, I want to know how much a pizza would cost if I had 15 toppings. One option is to continue the pattern. The pattern starts at 10 and increases by 1.50 each time. This could take a long time. Instead, we can write an equation and solve the equation for 15 toppings: $$y=mx+b$$ $$y=1.5x+10$$ Here, x represents the number of toppings and y represents the cost. We want to know the cost when $$x=15$$. Plug in and solve: $$y=1.5x+10$$ $$y=1.5(15)+10$$ $$y=22.50+10$$ $$y=32.50$$ Therefore, the cost of a pizza with $$15$$ toppings is $$y = 32.50$$. We can also use the equation to solve for the number of toppings given the price. How many toppings are on the pizza if the price of the pizza was $$19$$. We want to know the number of toppings when $$y=19$$. Plug in and isolate for x: $$y=1.5x+10$$ $$19=1.5x+10$$ $$19-10=1.5x$$ $$9=1.5x$$ $$9/1.5=x$$ $$6=x$$ Therefore, there were $$6$$ toppings if the pizza cost $$y = 19.00$$. Given the table of values for x and y, solve for when x = 40.  X Y 1 2 3 4 5 6 7 2 5 8 11 14 17 20 Using the same table as the question above, what would be the x value when y = 40? Gabriel's internet bill is$30/ month plus \$10/GB for every data over the limit (25 GB). Write a linear equation to represent Gabriel's bill.