Question

the point (2, 5) is represented on the graph. which point also belongs on this graph? (32, 35) (75, 30) (85, 34) (32, 80)

Explanation:

Step1: Find the slope of the line

The line passes through $(0,0)$ and $(2,5)$. Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5-0}{2-0} = \frac{5}{2}$

Step2: Write the line equation

Since it passes through the origin, the equation is $y = mx = \frac{5}{2}x$

Step3: Test each option

For $(32,80)$: Substitute $x=32$ into $y=\frac{5}{2}x$, we get $y=\frac{5}{2} \times 32 = 80$, which matches the point.

Answer:

(32, 80)