Question

Mr. Gilmore sells furniture. He earned $210 for selling 3 sofas. Mr. Gilmore
earned $570 for selling ll sofas. Which of the following equations represents this
situation, where s represents the number of sofas Mr. Gilmore sold and e
represents the amount he earned?

Answer 1

Let s represent the number of sofas and e  represent the amount earned.

We have been given that Mr. Gilmore sells furniture. He earned $210 for selling 3 sofas. Mr. Gilmore  earned $570 for selling 11 sofas. We are asked to write the equation for given scenario.

We have two points on a line that are (3,210) and (11,570).

Let us find slope of line passing through these points.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{570-210}{11-3}$

$m=\frac{360}{8}$

$m=45$

Now we will use point-slope form of equation.

$y-y_1=m(x-x_1)$, where

m = Slope,

$(x_1,y_1)$ = Any point on line.

$y-210=45(x-3)$

$y-210=45x-135$

$y-210+210=45x-135+210$

$y=45x+75$

Since amount earned is e and number of sofas is s, so our equation would be $e=45s+75$.

Therefore, our required equation would be $e=45s+75$.