Step-by-step explanation:
Write the equation in the form of Y=mX+C so that it is easuer to find the gradientor slope
[tex]y - 1 = - 2(x + 5) \\ y - 1 = - 2x - 10 \\ y = - 2x - 9[/tex]
the slope is -2 .
since we need to find a perpendicular equation, the gradient or slope should be negative reciprocal of the gradient we have now which is -2
the perpendicular gradient = 1/2
coordinates: (-3,2)
[tex]y - y1 = m(x - x1) \\ y - 2 = \frac{1}{2} (x - ( - 3)) \\ 2y - 4 = x + 3 \\ 2y = x + 7[/tex]
Answer:
y - 2 = [tex]\frac{1}{2}[/tex] (x + 3)
Step-by-step explanation:
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
y - 1 = - 2(x + 5) ← is in point- slope form
with slope m = - 2
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}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
and (a, b) = (- 3, 2), thus
y - 2 = [tex]\frac{1}{2}[/tex](x - (- 3) ), that is
y - 2 = [tex]\frac{1}{2}[/tex](x + 3) ← equation of perpendicular line
