True North Math
HomeTopicsInequalities & GraphingSlope (Positive & Negative)
Back to all topics

Inequalities & Graphing

Slope (Positive & Negative)

Slope measures the steepness of a line. It equals rise over run: m = (y₂ − y₁) / (x₂ − x₁). Positive slope goes up left to right; negative slope goes down.

✨ Rise over run — think of hiking up or down a hill!

Visualize It

Positive vs Negative Slope

m=1 (positive)m=−2 (negative)m=0 (horizontal)xy-8-8-6-6-4-4-2-2224466880

Watch & Learn

Watch a clear, friendly video explanation of Slope (Positive & Negative):

Watch on YouTube →

Opens a YouTube search for the best tutorial videos on this topic.

Worked Examples

Follow along with these step-by-step examples. Take your time — there's no rush!

1Example 1

Problem

Find the slope between (2, 3) and (6, 7)

Step-by-Step Solution

1

Use the formula: m = (y₂ − y₁) / (x₂ − x₁)

2

m = (7 − 3) / (6 − 2)

3

m = 4 / 4 = 1

4

Positive slope — line goes up left to right.

Answer

m = 1

Points (2,3) and (6,7) — slope = 1

m=1xy-8-8-6-6-4-4-2-2224466880(2,3)(6,7)
2Example 2

Problem

Find the slope between (1, 5) and (4, −1)

Step-by-Step Solution

1

m = (−1 − 5) / (4 − 1)

2

m = −6 / 3 = −2

3

Negative slope — line goes down left to right.

Answer

m = −2

Points (1,5) and (4,−1) — slope = −2

m=−2xy-8-8-6-6-4-4-2-2224466880(1,5)(4,−1)
3Example 3

Problem

What is the slope of a horizontal line?

Step-by-Step Solution

1

A horizontal line has no rise — it stays flat.

2

Rise = 0, so slope = 0/run = 0.

Answer

m = 0

Horizontal line y = 2 — slope = 0

m=0xy-8-8-6-6-4-4-2-2224466880(−3,2)(3,2)
4Example 4

Problem

Find the slope between (3, −2) and (3, 5)

Step-by-Step Solution

1

m = (y₂ − y₁) / (x₂ − x₁)

2

m = (5 − (−2)) / (3 − 3)

3

m = 7 / 0

4

Division by zero — slope is undefined.

5

Vertical lines always have undefined slope.

Answer

Undefined (vertical line)

Vertical line x = 3 — undefined slope

x=3xy-8-8-6-6-4-4-2-2224466880(3,−2)(3,5)
5Example 5

Problem

Find the slope between (−3, −2) and (1, 6)

Step-by-Step Solution

1

m = (6 − (−2)) / (1 − (−3))

2

m = 8 / 4 = 2

3

Positive slope — line rises left to right.

Answer

m = 2

Points (−3,−2) and (1,6) — slope = 2

m=2xy-8-8-6-6-4-4-2-2224466880(−3,−2)(1,6)

Your Turn — Practice Problems

Try all 5 problems on your own first. Write out your work — that's how it sticks!

💡 Tip: Don't peek at the answers until you've genuinely tried each one.

1

Find slope between (0, 0) and (3, 6)

(0,0) and (3,6)

m=2xy-8-8-6-6-4-4-2-2224466880(0,0)(3,6)
2

Find slope between (2, 8) and (5, 2)

(2,8) and (5,2)

m=−2xy-8-8-6-6-4-4-2-2224466880(2,8)(5,2)
3

Find slope between (−1, 3) and (3, 3)

(−1,3) and (3,3)

m=0xy-8-8-6-6-4-4-2-2224466880(−1,3)(3,3)
4

Find slope between (4, 1) and (4, 7)

(4,1) and (4,7) — vertical

x=4 (undefined)xy-8-8-6-6-4-4-2-2224466880(4,1)(4,7)
5

Find slope between (−2, −4) and (2, 4)

(−2,−4) and (2,4)

m=2xy-8-8-6-6-4-4-2-2224466880(−2,−4)(2,4)
6

Find slope between (1, 5) and (3, 9)

(1,5) and (3,9)

m=2xy-8-8-6-6-4-4-2-2224466880(1,5)(3,9)
7

Find slope between (0, 6) and (3, 0)

(0,6) and (3,0)

m=−2xy-8-8-6-6-4-4-2-2224466880(0,6)(3,0)
8

Find slope between (−4, 2) and (0, 6)

(−4,2) and (0,6)

m=1xy-8-8-6-6-4-4-2-2224466880(−4,2)(0,6)
9

Is a slope of 5 steeper than a slope of 2?

Steeper slope: m=5 vs m=2

m=5 (steeper)m=2xy-8-8-6-6-4-4-2-2224466880
10

What does a negative slope tell you about a line?

Negative slope goes downward

negative slopepositive slopexy-8-8-6-6-4-4-2-2224466880
11

Find slope between (3, −1) and (7, −1)

(3,−1) and (7,−1)

m=0xy-8-8-6-6-4-4-2-2224466880(3,−1)(7,−1)
12

Find slope between (5, 2) and (5, −3)

(5,2) and (5,−3) — vertical

x=5 (undefined)xy-8-8-6-6-4-4-2-2224466880(5,2)(5,−3)

Finished all 12? Give yourself a pat on the back — then check your work!

Keep going — you're on a roll!

Every topic you master is another step on your journey.

Explore More Topics