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How to Solve Slope-Intercept Form

Slope-intercept form is the most useful way to write a line: y = mx + b. You can read the slope and intercept instantly, then solve or graph with confidence.

📏 Algebra⏱️ ~14 min read🟢 Beginner

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What Does y = mx + b Mean?

In y = mx + b:

  • m is the slope (rise/run). If m = 3, then when x increases by 1, y increases by 3.
  • b is the y-intercept. It’s where the line crosses the y-axis (the point (0, b)).

If you’re new to linear functions in general, start with how to solve linear functions.

Step 1: Identify Slope and Intercept

Example: y = -2x + 5

  • Slope: m = -2
  • y-intercept: b = 5 → point (0, 5)

Negative slope means the line goes down as x increases.

Step 2: Convert From Standard Form

Standard form is Ax + By = C. To convert to slope-intercept form, solve for y.

Example: 3x + 2y = 12

3x + 2y = 12
2y = -3x + 12
y = (-3/2)x + 6

Now you can read slope m = -3/2 and intercept b = 6.

Step 3: Write y = mx + b From Two Points

If you have two points, first find the slope: m = (y2 - y1) / (x2 - x1).

Points: (1, 4) and (5, 12)

  1. Slope: m = (12 - 4) / (5 - 1) = 8/4 = 2.
  2. Use y = mx + b with a point (plug in x and y):
    4 = 2(1) + b
    b = 2
  3. Final equation: y = 2x + 2.

Step 4: Solve With the Equation

Find y from x

Example: y = 2x + 2, find y when x = 7

y = 2(7) + 2 = 16

Find x from y

Example: y = 2x + 2, find x when y = 18

18 = 2x + 2
16 = 2x
x = 8

Common Mistakes

Swapping slope and intercept

In y = mx + b, the number attached to x is the slope. The constant is the intercept.

Forgetting to divide both terms

When solving for y from Ax + By = C, divide every term on the right by B.

Using x2 - x1 = 0

If two points share the same x-value, the line is vertical and cannot be written as y = mx + b.

Dropping negative signs

Keep parentheses when computing slope and when moving terms.

For more worked examples converting between forms (and connecting the equation to the graph), you can also skim Khan Academy’s linear equations & inequalities lessons.

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How to Solve Slope-Intercept Form (y = mx + b) | Step-by-Step