Given two points that the line goes through,
y intercept of 2, this corresponds to (0, 2)
(4, -1)
We have,
[tex]\begin{gathered} (x_1,y_1)=(0,2) \\ (x_2,y_2)=(4,-1) \end{gathered}[/tex]The point slope formula is,
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope and,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, let's substitute the points into the point slope form of the line and re-arrange to slope intercept form. The steps are shown below:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-2=\frac{-1-2}{4-0}(x-0) \\ y-2=-\frac{3}{4}(x-0)-------\text{ Point Slope Form} \\ -------------------------------------- \\ \text{Then, we re-arrange to slope intercept form (y = mx + b):} \\ y-2=-\frac{3}{4}(x) \\ y-2=-\frac{3}{4}x \\ y=-\frac{3}{4}x+2----------\text{Slope Intercept Form} \\ -------------------------------------- \end{gathered}[/tex]Answer[tex]\begin{gathered} y-2=-\frac{3}{4}(x-0)-------\text{ Point Slope Form} \\ y=-\frac{3}{4}x+2----------\text{Slope Intercept Form} \end{gathered}[/tex]