Notice that the line passes through the points (2,0) and (-2,3), then, we can find the slope of the line with the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
in this case,we have the following:
[tex]\begin{gathered} m=\frac{3-0}{-2-2}=-\frac{3}{4} \\ \Rightarrow m=-\frac{3}{4} \end{gathered}[/tex]
then, using the slope-point form with the point (2,0) and m = -3/4, we get:
[tex]\begin{gathered} y-0=-\frac{3}{4}(x-2)=-\frac{3}{4}x+\frac{6}{4}=-\frac{3}{4}x+\frac{3}{2} \\ \Rightarrow y=-\frac{3}{4}x+\frac{3}{2} \end{gathered}[/tex]
therefore, the slope intercept form of the equation is y = -3/4x+3/2
