In the xy-plane, line k passes through the point (2, -3) and has a slope of -\frac{4}{3}. … — GRE General Test

In the $xy$ -plane, line $k$ passes through the point $(2, -3)$ and has a slope of $-\frac{4}{3}$ . Line $m$ is parallel to line $k$ and has an $x$ -intercept at $(6, 0)$ . What is the $y$ -intercept of line $m$ ?

$8$ Answer
B
$-8$
C
$\frac{9}{2}$
D
$\frac{3}{4}$
E
$-6$

Answer

The

y

-intercept of line

m

8

Parallel lines have equal slopes, so line

m

has slope

m = -\frac{4}{3}

. An

x

-intercept of

(6, 0)

means line

m

passes through

(6, 0)

. Substituting

x = 6

y = 0

, and

m = -\frac{4}{3}

into

y = mx + b

gives

0 = -\frac{4}{3}(6) + b

, which simplifies to

0 = -8 + b

, so

b = 8

. Thus, the

y

-intercept is

8

Step-by-Step Solution

Determine the slope of line

m

The slope of line

m

-\frac{4}{3}

Parallel lines in the coordinate plane have identical slopes. Since line

k

has a slope of

-\frac{4}{3}

, line

m

must also have a slope of

-\frac{4}{3}

Use the

x

-intercept

(6, 0)

to solve for the

y

-intercept

b

of line

m

0 = -\frac{4}{3}(6) + b \implies 0 = -8 + b \implies b = 8

Substitute

x = 6

y = 0

, and slope

m = -\frac{4}{3}

into the slope-intercept form

y = mx + b

Key Concept

Parallel line slopes and slope-intercept form

Estimated Time:1m 15s

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