Stage 5 · Points, Slopes, Lines & Graphs

Finding Slope

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 (+)
↗ uphill
Line goes up as you move right.
The car is going uphill.
Negative slope (−)
↘ downhill
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).

-4-4-2-22244
Find the perfect crossing points
-4-4-2-22244
These are the points we use
📐 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.

rise=+4 run=6

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
📋 Open Formula Sheet
Practice — Slope from a Graph
Questions are random — answer as many as you like
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Part 2 — Slope from a Table

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.

x y 0 1 2 4 4 7 6 10 +2 +2 +2 +3 +3 +3 Δx = +2 Δy = +3
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
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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.
Practice — Slope from Two Points
Questions are random — answer as many as you like
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Up Next in Points, Slopes, Lines & Graphs
Graphing Lines & Writing Equations
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