Question

what is the equation of the line?
for any proportional relationship, the equation of the line is $y = mx$, where $m$ is the slope of the line.
$y = 1.5x$ $y = 3x$
$y = 15x$ $y = 30x$
(chart: total cost ($) on y - axis, number of months on x - axis, line passing through (0,0) and (2,60))

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the origin \((0,0)\) and the point \((2, 60)\) (since at \(x = 2\) months, the total cost \(y=60\) dollars).

Step2: Calculate the slope \(m\)

The formula for the slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Using the points \((0,0)\) and \((2,60)\), we substitute \(x_1 = 0,y_1 = 0,x_2=2,y_2 = 60\) into the formula:
\(m=\frac{60 - 0}{2 - 0}=\frac{60}{2}=30\)

Step3: Write the equation of the line

For a proportional relationship, the equation of the line is \(y=mx\), where \(m\) is the slope. Since \(m = 30\), the equation is \(y = 30x\).

Answer:

\(y = 30x\)