Graphs · y = mx + b · 5.3

Graph a line.

To graph y = mx + b, plot the y-intercept (0, b) first, then use the slope as rise/run to step to the next point, and draw the line. For y = 2x + 1, start at (0, 1), then up 2 over 1.

01 / THE IDEA

See it work.

Watch the method

Graph a line

Start at (0, b), then rise/run by m.

1 / 2
-6-666
1

Substitute x

Put x = 2 into the equation.

y=2x+1,  x=2y = 2x + 1,\; x = 2
2

Compute y

Evaluate to find y.

y=5y = 5
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.

Intercept then slope

The y-intercept gives a starting point; the slope tells you how to step to more points.

Why it works

From (0, 1), up 2, over 1.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

For y=2x-2, find y when x = 2.

1

Substitute x

Put x = 2 into the equation. y = 2x - 2, x = 2

2

Compute y

Evaluate to find y. y = 2

EX 2medium

For y=1x-2, find y when x = -2.

1

Substitute x

Put x = -2 into the equation. y = x - 2, x = -2

2

Compute y

Evaluate to find y. y = -4

EX 3hard

For y=1x+5, find y when x = -3.

1

Substitute x

Put x = -3 into the equation. y = x + 5, x = -3

2

Compute y

Evaluate to find y. y = 2

04 / COMMON TRAPS

Where students slip.

Trap

Starting at the origin always.

Fix

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

Trap

Using the slope upside down.

Fix

Rise over run: up by the numerator, over by the denominator.

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

For y=-3x+3, find y when x = -1.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
C2

For y=3x+3, find y when x = 1.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
C3

For y=2x+5, find y when x = -4.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
C4

For y=2x+3, find y when x = 2.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
Apply

Apply (4)

A1

For y=-3x+3, find y when x = -1.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
A2

For y=-1x+5, find y when x = -2.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
A3

For y=2x-2, find y when x = -3.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
A4

For y=1x-4, find y when x = -3.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
Extension

Extension (4)

E1

For y=3x+1, find y when x = 0.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
E2

For y=-3x+4, find y when x = 2.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
E3

For y=-3x-5, find y when x = 1.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.
E4

For y=-3x+2, find y when x = 1.

Need a hint?
  • Plot (0, b) first.
  • Step by the slope, then draw the line.