Reviewed by Phoebe Belza-Barrientos
A line contains points M(1, 3) and N(5, 0). What is the slope of MN?
Answer: The slope of MN is -0.75
The slope of a line passing through two points represents the rate of change between the y-values and x-values of those points. By using the slope formula, you can determine how steep the line segment MN is by comparing how much y changes for each unit of change in x.
Methods
Math Tutor Explanation Using the Slope Formula
The slope (m) of a line passing through two points is calculated using the formula m = (y2 - y1) / (x2 - x1). For points M(1, 3) and N(5, 0), substitute the coordinates into the formula.
Step 1: Step 1: Identify the coordinates: M(x1, y1) = (1, 3), N(x2, y2) = (5, 0)
Step 2: Step 2: Substitute into the formula: (0 - 3) / (5 - 1)
Math Tutor Explanation Using Visual Representation
By plotting the points M and N on a coordinate plane, the slope can be visually identified as the 'rise over run' between the two points.
Step 1: Step 1: Plot point M at (1, 3) and point N at (5, 0) on a graph
Step 2: Step 2: Draw the line connecting M and N
Step 1:
Step 2:
Math Tutor suggests: Practice Slope, Lines, and Coordinate Geometry
Strengthen your understanding of slopes, lines, and coordinate geometry with these related exercises.
FAQ on Finding the Slope of a Line
What does the slope represent?
The slope shows how much the y-value changes for each unit increase in the x-value.
What does a negative slope mean?
A negative slope means the line is decreasing as you move from left to right.
Can the slope be zero?
Yes, if the y-values are the same for both points, the line is horizontal and the slope is zero.
How do you know if a line is vertical?
If the x-values are the same for both points, the change in x is zero, leading to an undefined slope, which means the line is vertical.
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