In the xy-plane, line k is defined by the equation y = 3x - 4. Line L is perpendicular to … — GRE General Test

In the $xy$ -plane, line $k$ is defined by the equation $y = 3x - 4$ . Line $L$ is perpendicular to line $k$ and passes through the point $(6, 2)$ . What is the $y$ -intercept of line $L$ ?

A
$-16$
B
$-4$
$4$ Answer
D
$12$
E
$20$

Answer

The

y

-intercept of line

L

4

Line

k

has a slope of

3

. Since line

L

is perpendicular to line

k

, the slope of line

L

-\frac{1}{3}

. Substituting the point

(6, 2)

into the slope-intercept equation

y = mx + b

gives

2 = -\frac{1}{3}(6) + b

, which simplifies to

2 = -2 + b

, so

b = 4

. Therefore, the

y

-intercept is

4

Step-by-Step Solution

Find the slope of line

L

The slope of line

L

-\frac{1}{3}

Line

k

has equation

y = 3x - 4

, so its slope is

3

. Perpendicular lines have slopes that are negative reciprocals.

Substitute the point

(6, 2)

and slope

-\frac{1}{3}

into the slope-intercept form

2 = -\frac{1}{3}(6) + b \implies 2 = -2 + b

The equation of a line is

y = mx + b

, where

m

is the slope and

b

is the

y

-intercept.

Solve for

b

b = 4

Adding

2

to both sides yields the

y

-intercept.

Key Concept

Perpendicular Line Slopes and Slope-Intercept Form

Question

Answer

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