We have the graph of the equation, and we want to know the equation of the line.
We remember that we need to parts: the slope and the y-intercept. On the graph, we see that when x=0, the graph passes through the point 2, and thus the y-intercept is 2.
[tex]b=2[/tex]
Lastly, we will find the slope. For doing so, we will find two values of the line. In this case, we saw that the y-intercept is 2, so a point is (0,2).
Other point is (-4,0), as the x-intercept is -4.
For finding the slope, we remember the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{0-(-4)}=\frac{2}{4}=\frac{1}{2}[/tex]
And thus, the slope is 1/2.
This means that the line equation will be:
[tex]\begin{gathered} y=mx+b \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]
