Three ways to find slope — from a graph, from a table, and from two points — with practice on all three.
Part 1 — Slope from a Graph
A line on a graph has something called slope — it measures how fast the line goes up or down as it moves to the right. A line going uphill has a positive slope. A line going downhill has a negative slope.
Positive slope (+)
Line goes up as you move right. The car is going uphill.
Negative slope (−)
Line goes down as you move right. The car is going downhill.
Look at the grid behind the line. The line crosses through many grid intersections — those are the perfect crossing points we use to measure slope. We are going to measure two things: how much the line moves up or down (the rise), and how much it moves left or right (the run).
Find the perfect crossing points
These are the points we use
1Find two places where the line crosses a grid intersection perfectly — where it lands exactly on a corner, not between lines.
2Start at the lower point. Count straight up until you are level with the upper point. That number is the rise — it is always positive when you count up.
3Now count left or right to reach the upper point. Counting right is positive. Counting left is negative. That number is the run.
4Write the rise over the run as a fraction — rise on top, run on bottom: riserun
5Simplify the fraction if possible. That is your slope.
📐 Worked Example — Rise over Run
Find the slope of the line shown in the graph below. Use the grid to identify two perfect crossing points, then count the rise and run.
Points read from graph: (−3, −2) and (3, 2)
m = rise ÷ run
rise = 2 − (−2) = 4
run = 3 − (−3) = 6
m = 4 ÷ 6 = 2/3
💡Always reduce your fraction.46 = 23, not 46. If the bottom is 1, write a whole number: 41 = 4.
Reference
GED Formula Sheet
All formulas available on the real test — opens in a new tab
A table shows pairs of x and y values. If the relationship is linear (a straight line), the slope is always the same between any two rows.
Find slope from a table by calculating: Δy ÷ Δx — the change in y divided by the change in x.
slope = ΔyΔx = 32
You can use any two consecutive rows — the slope will always come out the same (if it's a linear relationship).
💡Watch the sign. If y is going down as x goes up, Δy is negative and the slope will be negative.
Practice — Slope from a Table
Questions are random — answer as many as you like
Loading questions…
Part 3 — Slope from Two Points
If you have two coordinate pairs, you can find slope using the slope formula. This formula is on your GED formula sheet — you do not need to memorize it.
m = y₂ − y₁x₂ − x₁
m = slope | (x₁, y₁) = first point | (x₂, y₂) = second point
📐 Worked Example — Two Points
Find the slope of the line through (2, 5) and (6, 1).
Label your points
(2x₁ , 5y₁)(6x₂ , 1y₂)
↓ plug into the formula
m = y₂ − y₁x₂ − x₁ = 1 − 56 − 2 = −44 = −1
m = (y₂ − y₁) ÷ (x₂ − x₁)
m = (1 − 5) ÷ (6 − 2)
m = −4 ÷ 4
m = −1
⚠️Watch for negatives! These problems frequently include negative coordinates. Write every number out on paper before you substitute — don't try to do it in your head. One sign mistake and you'll get the wrong answer.
🧮No-calculator section. Slope questions often appear where calculators aren't allowed. Practice doing the subtraction by hand. Once you're comfortable, try each question without a calculator first — then check your work.