Parallel and perpendicular slopes from slope-intercept form

Warm-upeasy

Line $p$ is defined by $y = -5x + 2$ . Line $q$ is parallel to line $p$ in the coordinate plane. What is the slope of line $q$ ?

Parallel lines have the same slope. In $y = -5x + 2$ , the slope is $-5$ , so the slope of line $q$ is also $-5\textsf{.}$

Mid-gameeasy

Line $m$ is defined by $y = \dfrac{3}{4}x + 8$ . Line $n$ is parallel to line $m$ in the coordinate plane. What is the slope of line $n$ ?

Parallel lines have the same slope. In $y = \dfrac{3}{4}x + 8$ , the slope is $\dfrac{3}{4}$ , so the slope of line $n$ is also $\dfrac{3}{4}\textsf{.}$

Mid-gameeasy

Line $a$ is defined by $y = -x + 11$ . Line $b$ is parallel to line $a$ in the coordinate plane. What is the slope of line $b$ ?

Parallel lines have the same slope. In $y = -x + 11$ , the slope is $-1$ , so the slope of line $b$ is also $-1\textsf{.}$

Mid-gameeasy

Line $c$ is defined by $y = \dfrac{5}{2}x - 9$ . Line $d$ is parallel to line $c$ in the coordinate plane. What is the slope of line $d$ ?

Parallel lines have the same slope. In $y = \dfrac{5}{2}x - 9$ , the slope is $\dfrac{5}{2}$ , so the slope of line $d$ is also $\dfrac{5}{2}\textsf{.}$

Mid-gameeasy

Line $j$ is defined by $y = -4x + 10$ . Line $o$ is perpendicular to line $j$ in the coordinate plane. What is the slope of line $o$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $j$ is $-4$ , so the slope of line $o$ is $\dfrac{1}{4}\textsf{.}$

Mid-gameeasy

Line $u$ is defined by $y = \dfrac{2}{5}x - 3$ . Line $v$ is perpendicular to line $u$ in the coordinate plane. What is the slope of line $v$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $u$ is $\dfrac{2}{5}$ , so the slope of line $v$ is $-\dfrac{5}{2}\textsf{.}$

Mid-gameeasy

Line $w$ is defined by $y = -\dfrac{1}{3}x + 4$ . Line $z$ is perpendicular to line $w$ in the coordinate plane. What is the slope of line $z$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $w$ is $-\dfrac{1}{3}$ , so the slope of line $z$ is $3\textsf{.}$

Buzzer beatereasy

Line $t$ is defined by $y = 5x - 8$ . Line $k$ is perpendicular to line $t$ in the coordinate plane. What is the slope of line $k$ ?

Perpendicular lines have slopes that are negative reciprocals. The slope of line $t$ is $5$ , so the slope of line $k$ is $-\dfrac{1}{5}\textsf{.}$

Parallel and perpendicular slopes from slope-intercept form. Game on.

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