Positive
Rises from left to right.
Formulas & graphing
Slope Formula
Slope tells how steep a line is and which direction it moves. It compares the vertical change, called rise, with the horizontal change, called run.
m =y₂ - y₁x₂ - x₁=riserun
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Slope Is All Around Us
Slope describes how steep something is and how quickly its height changes as it moves forward.
Read the direction
Four Types of Slope
Negative
Falls from left to right.
Zero
Horizontal line.
Undefined
Vertical line.
Worked example
Find the Slope Between (1, 2) and (4, 8)
Step 1: Label Both Points
(x₁, y₁) = (1, 2)
(x₂, y₂) = (4, 8)
Keep each point together.
Step 2: Follow the Top
y₂−y₁→8 − 2 = 6
The change in y is 6.
Step 3: Follow the Bottom
x₂−x₁→4 − 1 = 3
Use the same subtraction order.
Step 4: Divide and Simplify
Put the change in y over the change in x.
m = 6/3 = 2
Slope calculator
Find Slope From Two Points
Enter two points. The calculator shows every step.
Optional: Enter the two ordered pairs
Entering a value here also changes the matching value in the formula below.
m =
−
−
Step 1: Subtract y₂ - y₁8 - 2 = 6
Step 2: Subtract x₂ - x₁4 - 1 = 3
Step 3: Put the answers into the formulam = 63 = 2
Watch out
Common Mistakes
- Subtracting x-values on top instead of y-values.
- Changing the subtraction order halfway through.
- Calling a vertical line’s slope zero instead of undefined.
Memory tool
Rise Over Run
Vertical change goes on top. Horizontal change goes on the bottom.
Your turn
10-Question Slope Practice
Type the slope, slope type, or coordinate requested.
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