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Difficulty: EasyParallel and Perpendicular Lines

In the standard (x,y)(x, y) coordinate plane, line L1L_1 passes through the points (−1,2)(-1, 2) and (3,14)(3, 14). If line L2L_2 is parallel to line L1L_1, what is the slope of line L2L_2?

Answer: 3

Answer

The slope of line L2L_2 is 33.
To find the slope of line L2L_2, we calculate the slope of line L1L_1 using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Substituting the coordinates (−1,2)(-1, 2) and (3,14)(3, 14) yields m=14−23−(−1)=124=3m = \frac{14 - 2}{3 - (-1)} = \frac{12}{4} = 3. Because parallel lines have the same slope, the slope of line L2L_2 is also 33.

Step-by-Step Solution

1
Calculate the slope of line L1L_1 using the coordinates of the two given points, (−1,2)(-1, 2) and (3,14)(3, 14).
m=3m = 3
The slope formula is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, which evaluates to m=14−23−(−1)=124=3m = \frac{14 - 2}{3 - (-1)} = \frac{12}{4} = 3.
2
Determine the slope of line L2L_2 based on its relationship to line L1L_1.
The slope of line L2L_2 is 33.
Parallel lines always have identical slopes.

Key Concept

Parallel lines have the same slope.
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Topics

Parallel and Perpendicular Lines

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