Question12 Which line is parallel to the line $y=-2 x-3$ ? (a) $y=-2 x+2$ c. $y=2 x+2$ (b) $y=2 x-2$ (d) $y=-0.5 x-2$

Studdy Solution

STEP 1

1. Two lines are parallel if they have the same slope.
2. The given line is in slope-intercept form $y = mx + b$ , where $m$ is the slope.
3. We need to compare the slope of the given line with the slopes of the lines in the options.

STEP 2

1. Identify the slope of the given line.
2. Identify the slopes of the lines in the options.
3. Determine which line has the same slope as the given line.

STEP 3

Identify the slope of the given line $y = -2x - 3$ .
The slope $m$ is the coefficient of $x$ .
For the line $y = -2x - 3$ , the slope $m = -2$ .

STEP 4

Identify the slopes of the lines in the options:
(a) $y = -2x + 2$ : The slope $m = -2$ .
(b) $y = 2x - 2$ : The slope $m = 2$ .
(c) $y = 2x + 2$ : The slope $m = 2$ .
(d) $y = -0.5x - 2$ : The slope $m = -0.5$ .

STEP 5

Determine which line has the same slope as the given line.
The given line has a slope of $-2$ .
Compare with the slopes of the options:
(a) $m = -2$ (same slope)
(b) $m = 2$ (different slope)
(c) $m = 2$ (different slope)
(d) $m = -0.5$ (different slope)
The line that is parallel to $y = -2x - 3$ is option (a) $y = -2x + 2$ .
The solution is:
$\boxed{a}$

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