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Find Slope of Line Through (-2, 1) and (3, 1)
Mathematics
Grade 8 (Junior High)
Question Content
What is the slope of the line passing 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
Step 1: Recall the slope formula. The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
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Step 2: Identify the coordinates of the two points. Here, \( (x_1, y_1) = (-2, 1) \) and \( (x_2, y_2) = (3, 1) \).
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Step 3: Substitute the coordinates into the slope formula. Calculate \( y_2 - y_1 \): \( 1 - 1 = 0 \). Calculate \( x_2 - x_1 \): \( 3 - (-2) = 3 + 2 = 5 \).
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Step 4: Compute the slope: \( m = \frac{0}{5} = 0 \).
Knowledge Points Involved
1
Slope Formula
The slope \( m \) of a line through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is defined as \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( y_2 - y_1 \) is the 'rise' (change in \( y \)) and \( x_2 - x_1 \) is the 'run' (change in \( x \)).
2
Slope of Horizontal Lines
Horizontal lines have a constant \( y \)-value for all \( x \)-values. For a horizontal line, \( y_2 - y_1 = 0 \), so the slope \( m = \frac{0}{x_2 - x_1} = 0 \) (as long as \( x_2 \neq x_1 \)).
3
Coordinate Identification
To apply the slope formula, correctly identify the \( x \)- and \( y \)-coordinates of the two points. In this problem, the points are \( (-2, 1) \) (where \( x_1 = -2, y_1 = 1 \)) and \( (3, 1) \) (where \( x_2 = 3, y_2 = 1 \)).
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