In the standard (x, y) coordinate plane, line p is perpendicular to the line represented b… — ACT

In the standard $(x, y)$ coordinate plane, line $p$ is perpendicular to the line represented by the equation $y = -0.2x + 9$ . What is the slope of line $p$ ?

Answer: 5

Answer

The slope of line

p

5

The given line is in slope-intercept form

y = mx + b

with a slope of

-0.2

, which can be written as

-\frac{1}{5}

. The slope of any line perpendicular to this line is the negative reciprocal of

-\frac{1}{5}

, which is

5

Step-by-Step Solution

Identify the slope of the given line from its equation.

The slope of the line

y = -0.2x + 9

-0.2

(or

-\frac{1}{5}

The equation is in slope-intercept form

y = mx + b

, where the coefficient of

x

represents the slope

m

Calculate the slope of the perpendicular line.

The negative reciprocal of

-\frac{1}{5}

5

Perpendicular lines have slopes that are negative reciprocals of each other (

m_1 \cdot m_2 = -1

Key Concept

Perpendicular lines in the coordinate plane have slopes that are negative reciprocals of each other.

Estimated Time:45s

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