In the standard (x, y) coordinate plane, line j has the equation y = -\frac{1}{4}x + 7. If… — ACT

In the standard $(x, y)$ coordinate plane, line $j$ has the equation $y = -\frac{1}{4}x + 7$ . If line $k$ is perpendicular to line $j$ , what is the slope of line $k$ ?

Answer: 4

Answer

The slope of line

k

is 4.

The slope of the perpendicular line is

4

because the negative reciprocal of the given slope,

-\frac{1}{4}

, is

4

Step-by-Step Solution

Identify the slope of line

j

The slope of line

j

-\frac{1}{4}

The equation of line

j

is given in slope-intercept form,

y = mx + b

, where the coefficient of

x

represents the slope.

Calculate the negative reciprocal of the slope of line

j

to find the slope of perpendicular line

k

The slope of line

k

4

Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of

-\frac{1}{4}

-\frac{1}{-\frac{1}{4}} = 4

Key Concept

The slopes of perpendicular lines are negative reciprocals of each other.

Estimated Time:45s

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