perpendicular line

Question

write the equation of the line that is perpendicular to the line with a slope of -2 and passes through the point (-4,3). write your equation in slope intercept form

Answer 1

A line that is perpendicular to a line with a slope of -2 has a slope of 1/2 (negative reciprocal), that is (-2)(1/2) = -1.

So now we have m = 1/2 passing through the point (-4,3). At this juncture there are basically two choices: 1) use point-slope, 2) use slope-intercept.

1) Use point slope. That means in the formula y - y₁=m(x - x₁), m=1/2, x₁=-4, y₁=3.

y - 3 = 1/2 (x - (-4))

y - 3 = 1/2 (x + 4)

y - 3 = 1/2 x + 2

y = 1/2 x +2 +3

y = 1/2 x + 5, [this means the y-intercept is (0, 5)

2) Using y = mx +b

The fact that the line passes through (-4,3) means when x = -4, y = 3.

3 = 1/2 (-4) + b

3 = -2 + b

b = 5

So, y = 1/2 x + 5

Here is a Desmos graph showing lines with a slope of -2 and the line perpendicular to that line passing through (-4,3).

desmos.com/calculator/wp258i0946