Back to Exercise: Prove slope criteria for lines

Exercises: Prove Slope Criteria for Parallel and Perpendicular Lines

Work through each section in order. Write every line equation in slope-intercept form unless a problem says otherwise, and show the slope you used before writing the equation.

Grade 10·23 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-gpe-b-5

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Warm-Up: Review What You Know

These problems review slope skills you already have.

What is the slope of the line through $(-3, 4)$ and $(5, -2)$ ?

$-\frac{4}{3}$

$\frac{3}{4}$

$-\frac{3}{4}$

$\frac{4}{3}$

Two lines in the same plane are perpendicular when they:

Never meet, no matter how far they are extended in either direction.

Have slopes that are both negative, so they both fall from left to right.

Have one slope defined and one slope undefined, which is the only way a right angle can occur.

Intersect so that the angle formed at the intersection is a right angle.

Rewrite $4x - 2y = 10$ in slope-intercept form and enter the slope of the line.

Fluency Practice

A line has slope $\frac{5}{3}$ . What is the slope of every line parallel to it?

A line has slope $\frac{5}{3}$ . What is the slope of a line perpendicular to it?

$\frac{3}{5}$

$-\frac{3}{5}$

$\frac{5}{3}$

$-\frac{5}{3}$

Which pair of slopes belongs to two perpendicular lines?

$6$ and $-6$ , because the two slopes are opposites.

$\frac{2}{7}$ and $\frac{2}{7}$ , because the two slopes match exactly.

$\frac{3}{8}$ and $\frac{8}{3}$ , because the two slopes are reciprocals.

$\frac{9}{4}$ and $-\frac{4}{9}$ , because the two slopes are negative reciprocals.

Write the equation of the line through $(8, -5)$ that is parallel to $y = \frac{3}{4}x - 2$ . Give your answer in slope-intercept form.

Write the equation of the line through $(4, -3)$ that is perpendicular to $2x + 5y = 15$ . Give your answer in slope-intercept form.

Line $j$ passes through $(-6, 2)$ and $(2, -4)$ . The slope of line $j$ is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . A line perpendicular to $j$ has slope ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . The equation of the perpendicular line through $(3, -1)$ , in slope-intercept form, is $y = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $x - 5$ .

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