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 $y=\frac{2}{3} x+1$

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 $y=mx+1$

$\begin{aligned}-1 &=-3 m+1 \\-2 &=-3 m \\\frac{2}{3} &=m\end{aligned}$

Hence, the slope is $m=\frac{2}{3}$

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

$y=\frac{2}{3} x+1$

Hence, the equation that represents the function is $y=\frac{2}{3} x+1$