Question

What is the equation of a line that is perpendicular to the line y - 1 = -2 (x + 5) and

Answer 1

Step-by-step explanation:

Write the equation in the form of Y=mX+C so that it is easuer to find the gradientor slope

$y - 1 = - 2(x + 5) \\ y - 1 = - 2x - 10 \\ y = - 2x - 9$

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)

$y - y1 = m(x - x1) \\ y - 2 = \frac{1}{2} (x - ( - 3)) \\ 2y - 4 = x + 3 \\ 2y = x + 7$

Answer 2

Answer:

y - 2 = $\frac{1}{2}$ (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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-2}$ = $\frac{1}{2}$

and (a, b) = (- 3, 2), thus

y - 2 = $\frac{1}{2}$(x - (- 3) ), that is

y - 2 = $\frac{1}{2}$(x + 3) ← equation of perpendicular line