Question

Here is a graph of a linear function. Write the equation that describes that function. Express it in slope-intercept form.

Answer 1

The equation that represents the function is
`y=(2)/(3) x+1`

Step-by-step explanation:

The formula for slope-intercept form is given by

`y=mx+b`

where m is the slope and b is the y-intercept.

The y-intercept of a graph can be determined by the point where the line intersects the y- axis.

From the graph, we can see that the line intersects the y-axis at the point 1.

Thus,the y-intercept is
`b=1`

Hence, the equation becomes
`y=mx+1`

Now, we shall find the slope by substituting the value
`x=-3` and
`y=-1` in the equation
`y=mx+1`

`\begin{aligned}-1 &=-3 m+1 \\-2 &=-3 m \\(2)/(3) &=m\end{aligned}`

Hence, the slope is
`m=(2)/(3)`

Thus, substituting the slope in the slope-intercept formula, we get,

`y=(2)/(3) x+1`

Hence, the equation that represents the function is
`y=(2)/(3) x+1`