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.
Explore Math Support Options
Find the perfect academic boost for your child through our comprehensive homework assistance and engaging programs that make learning fun and effective
Math & reading from 1st to 12th grade
Looking for homework support for your child?
Choose kid's grade
Math & Reading for Grades 1–12
Build real confidence for your child with a Brighterly math or reading tutor.
