Question

In the graph below, tell whether y varies directlywith x. If so, give an equation for the graph.

Answer 1

ANSWER:

Y varies directly with X

$y=\frac{3}{2}x$

STEP-BY-STEP EXPLANATION:

The variation is direct, since as x increases, y increases and if x decreases, y decreases.

The form of the slope and y-intercept equation is as follows

$\begin{gathered} y=mx+b \\ m\text{ is the slope and b is y-intercetp} \end{gathered}$

The slope is calculated like this

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

Replacing the points (3,2) and (0,0)

$\begin{gathered} m=\frac{3-0}{2-0} \\ m=\frac{3}{2} \end{gathered}$

The y-intercept is 0, therefore the equation would be

$y=\frac{3}{2}x$