Graphs · Slope · 4.4

Slope from a graph.

To read slope off a graph, pick two points the line passes through cleanly, then count the rise (up/down) and run (across) between them and divide.

01 / THE IDEA

See it work.

Watch the method

Slope from a graph

Count up 6, over 3 → slope 2.

1 / 2
-6-666
1

Rise over run

Rise = change in y = 6; run = change in x = 3.

63\frac{6}{3}
2

Simplify

The slope is rise ÷ run.

m=2m = 2
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 5.

streak 0
best 0
-6-666
Your answer:
— / WHY IT WORKS

The idea underneath.

Count the grid

Choose lattice points, count squares up then across, and form rise ÷ run.

Why it works

Up 6, over 3 → 2.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Find the slope of the line through (-4,5) and (-5,3).

1

Rise over run

Rise = change in y = -2; run = change in x = -1. -2/-1

2

Simplify

The slope is rise ÷ run. m = 2

EX 2medium

Find the slope of the line through (6,4) and (6,6).

1

Rise over run

Rise = change in y = 2; run = change in x = 0. 2/0

2

Simplify

The slope is rise ÷ run. m = undefined

EX 3hard

Find the slope of the line through (2,-4) and (4,5).

1

Rise over run

Rise = change in y = 9; run = change in x = 2. 9/2

2

Simplify

The slope is rise ÷ run. m = 9/2

04 / COMMON TRAPS

Where students slip.

Trap

Picking points off the line.

Fix

Use points the line clearly passes through.

Trap

Counting run before rise in the fraction.

Fix

Rise on top, run on bottom.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Find the slope of the line through (1,2) and (-5,-2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
C2

Find the slope of the line through (-4,-6) and (4,2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
C3

Find the slope of the line through (-2,-3) and (-6,2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
C4

Find the slope of the line through (2,6) and (6,-2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
Apply

Apply (4)

A1

Find the slope of the line through (4,2) and (-3,6).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
A2

Find the slope of the line through (6,6) and (1,2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
A3

Find the slope of the line through (2,1) and (-1,-6).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
A4

Find the slope of the line through (-6,6) and (6,-4).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
Extension

Extension (4)

E1

Find the slope of the line through (4,-1) and (-4,-4).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
E2

Find the slope of the line through (5,1) and (6,6).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
E3

Find the slope of the line through (-3,1) and (-1,-2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.
E4

Find the slope of the line through (-3,-6) and (6,-2).

Need a hint?
  • Pick two clean points.
  • Count rise over run.