We will use the fact that two lines are perpendicular if the product of their slopes is -1, and that the slope-point form of the equation of a line is y=mx+b, where m is the slope and b is the y-intercept.
Now, the first step to solve this problem is to determine the slope of line JY, for that we will use the following formula:
[tex]s=\frac{y_1-y_2}{x_1-x_2},[/tex]
where y and x are the entries of two points on the line.
Using the above formula with the given points J and y we get, that the slope of the line JY is:
[tex]s=\frac{-4-5}{3-(-2)}=\frac{-9}{3+2}=\frac{-9}{5}=-\frac{9}{5}\text{.}[/tex]
Therefore, if S is the slope of the line perpendicular to JY then:
[tex]S\times-\frac{9}{5}=-1.[/tex]
Solving the above equation for S we get:
[tex]S=\frac{5}{9}\text{.}[/tex]
Finally, the slope-intercept form of the equation of the perpendicular line to JY is:
[tex]y=\frac{5}{9}x-10.[/tex]
Answer:
[tex]y=\frac{5}{9}x-10.[/tex]
