Question

The given line passes through the points and (-4, -3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?

Answer 1

The equation of the line is y - 3 = -2(x + 4)

Explanation:

* Lets explain how to solve the problem

- The slope of the line which passes through the points (x1 , y1) and

(x2 , y2) is
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

- The product of the slopes of the perpendicular lines = -1

- That means if the slope of a line is m then the slope of the

perpendicular line to this line is -1/m

- The point-slope of the equation is
`y - y_(1)=m(x - x_(1))`

* lets solve the problem

∵ A given line passes through points (-4 , -3) and (4 , 1)

∴ x1 = -4 , x2 = 4 and y1 = -3 , y2 = 1

∴ The slope of the line
`m=(1-(-3))/(4-(-4))=(1+3)/(4+4)=(4)/(8)=(1)/(2)`

- The slope of the line perpendicular to this line is -1/m

∵ m = 1/2

∴ The slope of the perpendicular line is -2

- Lets find the equation of the line whose slope is -2 and passes

through point (-4 , 3)

∵ x1 = -4 , y1 = 3

∵ m = -2

∵ y - y1 = m(x - x1)

∴ y - 3 = -2(x - (-4))

∴ y - 3 = -2(x + 4)

* The equation of the line is y - 3 = -2(x + 4)