How to Graph an Equation in Standard Form

How to Graph a Standard Form Equation in 4 Steps

1. Find the x-intercept. Replace y with 0 and solve for x. The point is (C/A, 0).
2. Find the y-intercept. Replace x with 0 and solve for y. The point is (0, C/B).
3. Plot both intercepts and draw the line. Use a ruler and extend the line past both points.
4. Check with a third point. Pick another x-value, solve for y, and make sure that point lands on your line. The slope of Ax + By = C is −A/B.

If you need the intercepts on their own first, see finding the x- and y-intercepts in standard form.

Worked Example: Graph 2x + 3y = 6

x-intercept: 2x + 3(0) = 6, so x = 3. Plot (3, 0).

y-intercept: 2(0) + 3y = 6, so y = 2. Plot (0, 2).

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

Check: the slope is −A/B = −2/3, so starting at (0, 2) you move down 2 and right 3 to reach (3, 0). For a third point, let x = 9: 2(9) + 3y = 6 gives 3y = −12, so y = −4. The point (9, −4) sits on the same line.

Special Cases to Watch For

• No y-term (B = 0): Ax = C is a vertical line, x = C/A. For example, 2x = 8 is the line x = 4.
• No x-term (A = 0): By = C is a horizontal line, y = C/B. For example, 3y = 9 is the line y = 3.
• C = 0: both intercepts are (0, 0), so you need a second point. For 2x − y = 0, x = 1 gives y = 2, so graph the line through (0, 0) and (1, 2).
• Fraction intercepts: 3x + 4y = 6 has intercepts (2, 0) and (0, 1.5). Plot the half-unit carefully, or choose an x-value that gives a whole-number y instead.

Prefer slope-intercept form? You can also convert a standard form equation to slope-intercept form and graph from the y-intercept and slope. To check your work, try the standard form calculator.

Practice: Graph Each Equation

Find both intercepts, plot them, draw the line, then compare with the answers.

1. 4x + 2y = 8
2. 3x + 5y = 15

Show answers

1. 4x + 2y = 8: x-intercept (2, 0), y-intercept (0, 4), slope −2.

2. 3x + 5y = 15: x-intercept (5, 0), y-intercept (0, 3), slope −3/5.

Basic Mathematics for Beginners 2026 The Ultimate Step by Step Guide and A Comprehensive Basic Math Refresher

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Method 2: Graph standard form using the slope

If the intercepts come out as messy fractions, switch to slope-intercept form. Solve for y, plot the y-intercept, then use the slope to find more points.

Example: graph 2x + 4y = −8.

1. Subtract 2x from both sides: 4y = −2x − 8.
2. Divide every term by 4: y = −½x − 2.
3. Plot the y-intercept (0, −2).
4. The slope is −½. From (0, −2), go down 1 and right 2 to reach (2, −3).
5. Draw a line through the points.

Check with the intercept method: setting y = 0 gives 2x = −8, so x = −4. Setting x = 0 gives 4y = −8, so y = −2. The line passes through (−4, 0) and (0, −2). Also, 2(2) + 4(−3) = 4 − 12 = −8, so (2, −3) is on the line.

Which method should you use?

Frequently Asked Questions

How do you graph 2x + 4y = −8?

Find the intercepts. If y = 0, then 2x = −8, so x = −4. If x = 0, then 4y = −8, so y = −2. Plot (−4, 0) and (0, −2) and draw a line through them. The slope is −½, which matches the slope-intercept form y = −½x − 2.

How do I graph 2x + 3y = 6?

Set y = 0 to get 2x = 6, so the x-intercept is (3, 0). Set x = 0 to get 3y = 6, so the y-intercept is (0, 2). Plot both points and connect them. The line falls from left to right with slope −2/3. The point (6, −2) also works as a check.

How do you find the slope from standard form?

For Ax + By = C, the slope is −A/B. In 3x − 4y = 12, the slope is −3/(−4) = 3/4. You can confirm by solving for y: −4y = −3x + 12, so y = (3/4)x − 3.

What if the equation has C = 0?

When C = 0, both intercepts are the origin, so the intercept method gives only one point. Pick another x-value instead. For 2x − y = 0, try x = 1: then y = 2. Draw the line through (0, 0) and (1, 2).

How do you graph standard form when A or B is zero?

If A = 0, the equation is By = C, which is a horizontal line, such as 3y = 9, or y = 3. If B = 0, it is Ax = C, a vertical line, such as 2x = 8, or x = 4.