Question

Which is an equation of a line that passes through the point (-4, 7) and is perpendicular to the line y = (1/2)x + 4

Answer 1

Find the slope of the perpendicular line:

$y = \dfrac{1}{2} x + b$

$\text {Slope = } \dfrac{1}{2}$

$\text {Slope =} \boxed {\text{negative reciprocal}} \text { of the slope of the original line}$

$\text {Perpendicular Slope = -2}$

Form the equation:

$y = mx + b$

$y = -2x + b$

Find y-intercept given that the line passed through (-4, 7):

$y = -2x + b$

$7 = -2(-4) + b$

$7 = 8 + b$

$b = 7 - 8$

$b = -1$

Form the equation:

$y = -2x - 1$

$\boxed {\boxed {Answer: y = -2x - 1}}$

Answer 2

First you want to find the slope in a reciprocal and turn it to a negative, which is negative 2.