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Difficulty: EasyParallel and Perpendicular Lines

A straight road on a map is modeled by the linear equation 2x−5y=102x - 5y = 10 in the standard (x,y)(x, y) coordinate plane. A second road, which is parallel to the first road, is being constructed. What is the slope of the second road?

  1. A
    22
  2. B
    −52-\frac{5}{2}
  3. 25\frac{2}{5}Answer
  4. D
    −25-\frac{2}{5}
  5. E
    52\frac{5}{2}

Answer

The slope of the second road is 25\frac{2}{5}
Parallel lines have the same slope. Rewriting the line's equation 2x−5y=102x - 5y = 10 into slope-intercept form (y=mx+by = mx + b) yields y=25x−2y = \frac{2}{5}x - 2. The slope of this line is the coefficient of xx, which is 25\frac{2}{5}. Therefore, any line parallel to it must also have a slope of 25\frac{2}{5}.

Step-by-Step Solution

1
Determine the relationship between the slopes of parallel lines.
Parallel lines have identical slopes.
Since the second road is parallel to the first, its slope must be equal to the slope of the first road.
2
Convert the equation of the first road, 2x−5y=102x - 5y = 10, into slope-intercept form (y=mx+by = mx + b).
Subtract 2x2x from both sides to get −5y=−2x+10-5y = -2x + 10. Then, divide both sides by −5-5 to get y=25x−2y = \frac{2}{5}x - 2.
In slope-intercept form, the coefficient of xx (represented by mm) is the slope of the line.
3
Identify the slope of the first road and match it to the parallel road.
The slope of the first road is 25\frac{2}{5}, so the slope of the parallel road is also 25\frac{2}{5}.
The slope is the coefficient of xx, which is 25\frac{2}{5}.

Key Concept

Parallel lines in a coordinate plane have equal slopes.
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Topics

Parallel and Perpendicular Lines

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