The equation of the line in slope-intercept form has the next form
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
First we need to calculate the slope of the perpendicular line that passes through (3,2) and (-2,4) using the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where (x1,y1) and (x2,y2) are two points where the line passes through
In our case
(3,2)=(x1,y1)
(-2,4)=(x2,y2)
we substitute the values
[tex]m=\frac{4-2}{-2-3}=\frac{2}{-5}=-\frac{2}{5}[/tex]
The slope of our line needs to be the inverse to the slope we just found
[tex]m_p=\frac{5}{2}[/tex]
Then we need to find the y-intercept using x=1 and y=1
[tex]1=\frac{5}{2}(1)+b[/tex][tex]b=1-\frac{5}{2}=\frac{2}{2}-\frac{5}{2}=-\frac{3}{2}[/tex]
The equation of the line is
[tex]y=\frac{5}{2}x-\frac{3}{2}[/tex]
ANSWER
[tex]y=\frac{5}{2}x-\frac{3}{2}[/tex]
