Linear · Graphing lines · 3.1

Graph from y = mx + b.

To graph a line in slope-intercept form, plot the y-intercept (0, b), then use the slope as rise/run to step to another point, and draw the line through them.

01 / THE IDEA

See it work.

Watch the method

Graph from y = mx + b

Plot (0, b), then step by the slope.

1 / 2
y=2x−1y = 2x - 1
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1

Plot the y-intercept

Start at (0, -1).

(0, −1)(0,\, -1)
2

Use the slope

Rise/run by the slope to the next point, then draw the line.

m=2m = 2
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type y = mx + b.

streak 0
best 0
-8-888
…
Answer:
— / WHY IT WORKS

The idea underneath.

Intercept then slope

Start at the y-intercept and use rise/run to reach more points.

Why it works

From (0, −1), up 2, over 1.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Give the equation graphed (it is y=-2x+2).

1

Plot the y-intercept

Start at (0, 2). (0,\, 2)

2

Use the slope

Rise/run by the slope to the next point, then draw the line. m = -2

EX 2medium

Give the equation graphed (it is y=x+6).

1

Plot the y-intercept

Start at (0, 6). (0,\, 6)

2

Use the slope

Rise/run by the slope to the next point, then draw the line. m = 1

EX 3hard

Give the equation graphed (it is y=-x+2).

1

Plot the y-intercept

Start at (0, 2). (0,\, 2)

2

Use the slope

Rise/run by the slope to the next point, then draw the line. m = -1

04 / COMMON TRAPS

Where students slip.

Trap

Starting at the origin.

Fix

Start at the y-intercept (0, b).

Trap

Slope upside down.

Fix

Rise over run.

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

Give the equation graphed (it is y=2x+6).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
C2

Give the equation graphed (it is y=-2x-6).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
C3

Give the equation graphed (it is y=3x-4).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
C4

Give the equation graphed (it is y=2x-1).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
Apply

Apply (4)

A1

Give the equation graphed (it is y=-2x+1).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
A2

Give the equation graphed (it is y=2x+1).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
A3

Give the equation graphed (it is y=x-5).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
A4

Give the equation graphed (it is y=3x+1).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
Extension

Extension (4)

E1

Give the equation graphed (it is y=3x-5).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
E2

Give the equation graphed (it is y=-x+1).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
E3

Give the equation graphed (it is y=x+6).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.
E4

Give the equation graphed (it is y=-3x+6).

Need a hint?
  • Plot (0, b).
  • Step by rise/run.