Answer:
[tex]y=-\frac{3}{2}x-\frac{9}{2}[/tex]
Step-by-step explanation:
Let the equation of the perpendicular line is,
y = mx + b
where m = slope of the line
b = y-intercept
From the graph, slope of the line passing through (0, -1) and (3, 1),
m' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m' = [tex]\frac{1+1}{3-0}[/tex]
m' = [tex]\frac{2}{3}[/tex]
To get the slope (m) of this line we will use the property of perpendicular lines,
m × m' = (-1)
m × [tex]\frac{2}{3}[/tex] = -1
m = [tex]-\frac{3}{2}[/tex]
Equation of the perpendicular line will be,
[tex]y=-\frac{3}{2}x+b[/tex]
x-intercept of the line is (-3) therefore, point on the line is (-3, 0)
0 = [tex]-\frac{3}{2}(-3)+b[/tex]
b = [tex]-\frac{9}{2}=-4.5[/tex]
Equation of the line will be,
[tex]y=-\frac{3}{2}x-\frac{9}{2}[/tex]
