1Cademy - Verifying that $$y = -3x + 2$$ and $$x

Learn Before

Verifying that $y = -5x - 4$ and $x - 5y = 5$ are Perpendicular

Example

Verifying that $y = -3x + 2$ and $x - 3y = 4$ are Perpendicular

To determine whether the lines $y = -3x + 2$ and $x - 3y = 4$ are perpendicular, rewrite each equation in slope-intercept form and check if their slopes are negative reciprocals.

First equation: $y = -3x + 2$ is already in slope-intercept form. Its slope is $m_1 = -3$ .

Second equation: Solve $x - 3y = 4$ for $y$ . Subtract $x$ from both sides: $-3y = -x + 4$ Divide every term by $-3$ : $y = \frac{1}{3}x - \frac{4}{3}$ The slope is $m_2 = \frac{1}{3}$ .

Check for negative reciprocals: The slopes $-3$ and $\frac{1}{3}$ have opposite signs and are reciprocals of each other. Verify by computing their product:

ight) = -1$$ Because the product of the slopes is $$-1$$, the lines are perpendicular.

Updated 2026-04-23

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related