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Difficulty: EasySlope of a Line

A straight hiking trail ascends a hill at a constant incline. On a coordinate grid where the units represent meters, the path of the trail is a straight line starting at the coordinate point (10,150)(10, 150) and ending at the coordinate point (90,190)(90, 190). What is the slope of this trail?

Answer: 0.5

Answer

The correct answer is 0.50.5 (or 12\frac{1}{2}).
The slope of a line is defined as the change in the yy-coordinates divided by the change in the xx-coordinates: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. By substituting the coordinates of the start of the trail (10,150)(10, 150) and the end of the trail (90,190)(90, 190), we calculate 190−15090−10=4080=0.5\frac{190 - 150}{90 - 10} = \frac{40}{80} = 0.5.

Step-by-Step Solution

1
Identify the coordinates from the problem statement.
(x1,y1)=(10,150)(x_1, y_1) = (10, 150) and (x2,y2)=(90,190)(x_2, y_2) = (90, 190)
To calculate the slope between two points, we first need to define their coordinates.
2
Recall the formula for the slope of a line passing through two points.
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
Slope represents the vertical change (rise) divided by the horizontal change (run).
3
Substitute the coordinate values into the slope formula and simplify.
m=190−15090−10=4080=0.5m = \frac{190 - 150}{90 - 10} = \frac{40}{80} = 0.5
Plugging the values into the formula yields the constant rate of change (slope) of the trail.

Key Concept

Slope of a Line
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Topics

Slope of a Line

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