Same Math › Grade 8 › Slope triangles
What is a slope triangle?
A slope triangle is a right triangle drawn under a line between two points. Its horizontal side is the run, its vertical side is the rise, and slope = rise ÷ run. Any slope triangle on the same line gives the same slope.
- Run: how far across.
- Rise: how far up (or down, which is negative).
- slope = rise ÷ run
Why schools teach it
It shows why slope is the same everywhere on a line
Eighth graders use similar triangles to explain why the slope between any two points on a line is the same (8.EE.B.6), and interpret slope as a rate of change (8.F.B.4).
Drawing the triangle stops the most common slope mistakes: flipping rise and run, and losing the negative sign when a line goes down.
At the kitchen table
What to say, and what to skip
Say this
Pick two points where the line crosses grid corners.
How far across? How far up or down?
Is the line going up or down from left to right?
Down means negative slope.Try a bigger triangle. Same slope?
Skip this
Run over rise.
It's rise over run: up-and-down first.- Using the formula before the picture.(y₂ − y₁) ÷ (x₂ − x₁) is the triangle written as numbers. Draw first.
- Ignoring the sign.A line going down to the right has a negative slope.
See it in action
Slope through (1, 2) and (4, 8)
Run: from x = 1 to x = 4
3Rise: from y = 2 to y = 8
6Slope = rise ÷ run
6 ÷ 3 = 2
Slope is also the k from proportional relationships when the line goes through (0, 0).
Free practice sheet
Make a slope triangle sheet
Loading practice sheet…
Fridge cheat sheets
Math Fridge Cheat Sheets
Every K–8 math method in one printable book (159 pages): a cheat sheet page like this guide, plus a practice sheet and its answer key for each, in Classic and handwritten Notebook styles. $9 one time, or all 7 subjects for $29.99. See all prices.
Teacher? This method has a classroom pack on TeachersPayTeachers: an anchor chart, a parent letter and practice sheets with answer keys, $4. See the pack
Parents: tell your child's teacher about this guide
Parents also ask
What does a slope of 0 look like?
A flat, horizontal line. There's no rise.
What about a vertical line?
Its run is 0, and you can't divide by 0, so its slope is undefined.
Why does any triangle give the same slope?
The triangles are similar: same shape, different sizes, so their rise-to-run ratios match.
How is slope used in real life?
Speed, cost per item, and how steep a ramp or road is are all slopes.