The equation that represents the function is [tex]y=\frac{2}{3} x+1[/tex]
Explanation:
The formula for slope-intercept form is given by
[tex]y=mx+b[/tex]
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 [tex]b=1[/tex]
Hence, the equation becomes [tex]y=mx+1[/tex]
Now, we shall find the slope by substituting the value [tex]x=-3[/tex] and [tex]y=-1[/tex] in the equation [tex]y=mx+1[/tex]
[tex]\begin{aligned}-1 &=-3 m+1 \\-2 &=-3 m \\\frac{2}{3} &=m\end{aligned}[/tex]
Hence, the slope is [tex]m=\frac{2}{3}[/tex]
Thus, substituting the slope in the slope-intercept formula, we get,
[tex]y=\frac{2}{3} x+1[/tex]
Hence, the equation that represents the function is [tex]y=\frac{2}{3} x+1[/tex]
