Question

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

Answer 1

Y varies directly with X

`y=(3)/(2)x`

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=(y_2-y_1)/(x_2-x_1)_{}`

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

`\begin{gathered} m=(3-0)/(2-0) \\ m=(3)/(2) \end{gathered}`

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

`y=(3)/(2)x`