The slope-intercep form is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. We can find m by means of the following formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where these values come from the given points,
[tex]\begin{gathered} (x_1,y_1)=(0,3) \\ (x_2,y_2)=(4,-2) \end{gathered}[/tex]Then, by substituting these values into the slope formula, we get
[tex]m=\frac{-2-3}{4-0}[/tex]which gives
[tex]m=-\frac{5}{4}[/tex]Then, our line equation has the form
[tex]y=-\frac{5}{4}x+b[/tex]Now, we can find b by subtituting one of the given point into our last equation, that is, If we substitute point (0,3) we obtain
[tex]\begin{gathered} 3=-\frac{5}{4}(0)+b \\ 3=b \end{gathered}[/tex]Then, the line equation in slope-intercept form is
[tex]y=-\frac{5}{4}x+3[/tex]