Question

18) Write an equation of the line that is perpendicular to the line y = 4x - 10 that passes through the point (-16, 2). A) y = - 1 4 x - 2 B) y = -4x + 6 C) y = - 1 4 x + 2 D) y = 4x + 2

Answer 1

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be perpendicular, their slopes have to be negative reciprocals of each other. (flip the sign +/- and the fraction(switch the numerator and the denominator))

For example:

Slope = 2 or  $\frac{2}{1}$

Perpendicular line's slope = $-\frac{1}{2}$  (flip the sign from + to - , and flip the fraction)

Slope = $-\frac{1}{3}$

Perpendicular line's slope = $\frac{3}{1}$  or  3  (flip the sign from - to +, and flip fraction)

y = 4x - 10     The slope is 4, so the perpendicular line's slope is $-\frac{1}{4}$.

Now that you know the slope, substitute/plug it into the equation.

y = mx + b

$y=-\frac{1}{4}x+b$   To find b, plug in the point (-16, 2) into the equation, then isolate/get the variable "b" by itself

$2=-\frac{1}{4}(-16)+b$  (two negative signs cancel each other out and become positive)

2 = 4 + b      Subtract 4 on both sides to get "b" by itself

2 - 4 = 4 - 4 + b

-2 = b

$y=-\frac{1}{4}x-2$     Your answer is A