Answer:
y = [tex]\frac{2}{3}[/tex] x - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{3}{2}[/tex] x - 1 ← is in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{2} }[/tex] = [tex]\frac{2}{3}[/tex]
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = [tex]\frac{2}{3}[/tex] and (a, b) = (9, - 2), thus
y - (- 2) = [tex]\frac{2}{3}[/tex](x - 9), that is
y + 2 = [tex]\frac{2}{3}[/tex](x - 9) ← in point- slope form
Distribute right side and rearrange
y + 2 = [tex]\frac{2}{3}[/tex] x - 6 ( subtract 2 from both sides )
y = [tex]\frac{2}{3}[/tex] x - 8 ← in slope- intercept form
