How do you graph a line from an equation?

Put a dot at b on the y-axis, step across 1 and up by the slope to mark the next dot, repeat for a third dot, and draw a straight line through them.

How do you graph a line with a fraction slope?

Use the top of the fraction as the rise and the bottom as the run. For a slope of 2/3, go up 2 and across 3. If the slope is negative, go down instead of up.

How do you graph an equation that is not in y = mx + b form?

Get y alone first. For 3x + 2y = 6, subtract 3x from both sides and divide by 2 to get y = −1.5x + 3, then graph it as usual.

How many points do you need to graph a line?

Two points are enough to draw a line, but a third point is a good check. If all three sit on one straight line, you probably did it right.

Part 7 of 10 · LinesSee the whole course

How to graph a line from its equation

By The Pip team · October 23, 2026 · 6 min read

Short answer

To graph y = mx + b, put a dot at b on the y-axis. From there, go across 1 and up m (down if m is negative) to mark the next dot. Repeat, then draw a straight line through the dots.

The steps

Get y alone. Make sure the equation looks like y = mx + b.
Start at b. Put a dot at (0, b) on the y-axis.
Step by the slope. Write the slope as rise ÷ run. Go across by the run, then up (or down) by the rise, and put a dot.
Repeat once more for a third dot.
Draw the line through the dots with a ruler, and extend it past them.

Try it. Pick an equation, then take the steps one at a time.

Steps taken 2

start (0, −1), then up 2 across 1

Two dots are enough to draw the line.

Example 1: y = 2x − 1

The y-intercept is −1, so the first dot is (0, −1). The slope is 2, which is 2 ÷ 1: up 2, across 1.

Start: (0, −1)
Up 2, across 1: (1, 1)
Up 2, across 1: (2, 3)

Draw the line through (0, −1), (1, 1) and (2, 3).

Example 2: a fraction slope, y = −⅔x + 4

Start at (0, 4). The slope is −2 ÷ 3. The top of the fraction is the rise and the bottom is the run: down 2, across 3.

Start: (0, 4)
Down 2, across 3: (3, 2)
Down 2, across 3: (6, 0)

Check one dot in the rule: at x = 3, y = −⅔ × 3 + 4 = −2 + 4 = 2. It works.

Example 3: the equation is not in y = mx + b form

Take 3x + 2y = 6. Get y alone first:

2y = −3x + 6
y = −1.5x + 3

Now b = 3 and the slope is −1.5, which is −3 ÷ 2: down 3, across 2.

Start: (0, 3)
Down 3, across 2: (2, 0)
Down 3, across 2: (4, −3)

Check the last dot in the original equation: 3(4) + 2(−3) = 12 − 6 = 6. It works.

Watch it explained in under a minute

The same idea, narrated step by step. Square version for sharing: download the 1:1 video.

The five mistakes to avoid

Starting at the origin every time. Always start at (0, b).
Going up for a negative slope. A negative slope goes down.
Flipping the fraction. A slope of −2/3 is down 2 across 3, not down 3 across 2.
Graphing before getting y alone. In 3x + 2y = 6, the 3 is not the slope.
Using only two dots with no check. A third dot that falls on the line tells you the first two were right.

Try it yourself

Name the first three dots for each line. Tap a question to see the answer.

1. y = x + 2

Start (0, 2). The slope is 1, up 1 across 1: (1, 3), then (2, 4).

2. y = −2x + 5

Start (0, 5). The slope is −2, down 2 across 1: (1, 3), then (2, 1).

3. y = ½x − 3

Start (0, −3). The slope is ½, up 1 across 2: (2, −2), then (4, −1).

Where graphing fits in

Graphing a line is slope-intercept form put to work, so if the letters m and b are new, read slope-intercept form explained first. Next in this course, we go the other way: write the equation of a line from two points.