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Line
m passes through the points
(2,2) and
(-4,4). Which equation represents a line that is parallel to line
m ?
(A)
y=-(1)/(3)x+7
(B)
y=(1)/(3)x-4
(C)
y=-(2)/(5)x-3
(D)
y=(2)/(5)x+9

$4$ . Line $m$ passes through the points $(2,2)$ and $(-4,4)$ . Which equation represents a line that is parallel to line $m$ ? $\newline$ (A) $y=-\frac{1}{3} x+7$ $\newline$ (B) $y=\frac{1}{3} x-4$ $\newline$ (C) $y=-\frac{2}{5} x-3$ $\newline$ (D) $y=\frac{2}{5} x+9$

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Write an equation for a parallel or perpendicular line

Full solution

Q.

4

. Line

m

passes through the points

(2,2)

and

(-4,4)

. Which equation represents a line that is parallel to line

m

?

\newline

(A)

y=-\frac{1}{3} x+7

\newline

(B)

y=\frac{1}{3} x-4

\newline

(C)

y=-\frac{2}{5} x-3

\newline

(D)

y=\frac{2}{5} x+9

Calculate slope: Find the slope of line $m$ using the points $(2,2)$ and $(-4,4)$ .\ Slope $(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{-4 - 2} = \frac{2}{-6} = -\frac{1}{3}.$
Identify parallel lines: Parallel lines have the same slope. $\newline$ So, the slope of the line parallel to line $m$ is also $-\frac{1}{3}$ .
Check options: Check the options for a line with a slope of $-\frac{1}{3}$ . $\newline$ (A) $y = -\left(\frac{1}{3}\right)x + 7$ (slope is $-\frac{1}{3}$ , matches) $\newline$ (B) $y = \left(\frac{1}{3}\right)x - 4$ (slope is $\frac{1}{3}$ , does not match) $\newline$ (C) $y = -\left(\frac{2}{5}\right)x - 3$ (slope is $-\frac{2}{5}$ , does not match) $\newline$ (D) $y = \left(\frac{2}{5}\right)x + 9$ (slope is $\frac{2}{5}$ , does not match)
Select correct answer: The correct answer is the one with the slope $-\frac{1}{3}$ , which is option $(A)$ .

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