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Find the slope of the line through (-2,1) and (3,1)
Mathematics
Middle School (e.g., Grade 7)
Question Content
What is the slope of this line? The line passes through the points (-2, 1) and (3, 1). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Detailed Solution Steps
1
Recall the slope formula: The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2
Identify the coordinates of the two points: Let \( (x_1, y_1) = (-2, 1) \) and \( (x_2, y_2) = (3, 1) \).
3
Calculate the change in \( y \) (vertical change): \( y_2 - y_1 = 1 - 1 = 0 \).
4
Calculate the change in \( x \) (horizontal change): \( x_2 - x_1 = 3 - (-2) = 3 + 2 = 5 \).
5
Substitute the values into the slope formula: \( m = \frac{0}{5} = 0 \).
Knowledge Points Involved
1
Slope Definition
Slope measures the steepness of a line, defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line: \( m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} \).
2
Slope Formula
The formula for the slope \( m \) of a line through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). It is used to calculate the slope when two points on the line are known.
3
Slope of a Horizontal Line
A horizontal line has a constant \( y \)-value for all \( x \)-values. For such a line, the vertical change (\( y_2 - y_1 \)) is 0, so the slope is \( \frac{0}{\text{run}} = 0 \) (where 'run' is the horizontal change, a non - zero value).
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