Slope-intercept form is the linear equation form y = mx + b, where m is the slope and b is the y-intercept. You can read both values directly from the equation without rearranging: in y = 2x + 5, the slope is 2 and the line crosses the y-axis at (0, 5).
In Spanish
forma pendiente-intersección
Also called
y equals mx plus b, y = mx + b form, slope-intercept equation
To graph y = 23x + 1, start at the y-intercept (0, 1), then use the slope: go right 3 and up 2 to reach the next point, (3, 3).
Formal definition and notation
A non-vertical line with slope m that crosses the y-axis at the point (0, b) has the equation y = mx + b, where m and b are real numbers. Every non-vertical line has exactly one equation in this form. A vertical line x = a has no slope-intercept form because its slope is undefined.
In a word problem, b is the starting amount (a fixed fee) and m is the rate (dollars per hour, miles per gallon).
Slope-intercept form
Slope-intercept form
y = mx + b
m
the slope, riserun: how much y changes when x goes up by 1
b
the y-intercept: the value of y when x = 0
x, y
the coordinates of any point on the line
The equation must be solved for y first. In 2y = 6x + 4, divide every term by 2 to get y = 3x + 2 before you read m = 3 and b = 2.
Try it: build y = mx + b
Interactive
Drag point A or B and watch the equation y = mx + b change. Notice where the line crosses the y-axis: that is b. Try the presets, including the vertical line that has no slope-intercept form.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Slope-Intercept Form examples, step by step
Example 1: Read the slope and y-intercept
Warm-up
Find the slope and the y-intercept of y = 12x − 4.
Match the equation to y = mx + b.
The coefficient of x is 12, so m = 12.
The constant term is −4 (keep the minus sign), so b = −4 and the line crosses the y-axis at (0, −4).
Answer: The slope is 1/2 and the y-intercept is −4, the point (0, −4).
Example 2: Rewrite an equation in slope-intercept form
Core
Write 3x + 2y = 10 in slope-intercept form. Then name the slope and the y-intercept.
Get the y term alone: subtract 3x from both sides. 2y = −3x + 10.
Divide every term by 2: y = −32x + 5.
Read the values: m = −32 and b = 5.
Check with a point: when x = 2, y = −3 + 5 = 2, and 3(2) + 2(2) = 10. It works.
Answer: y = −(3/2)x + 5. The slope is −3/2 and the y-intercept is 5.
Example 3: Equation of a line through two points
Test-style
A line passes through (2, 7) and (6, −1). Which equation in slope-intercept form describes the line?
Find the slope: m = −1 − 76 − 2 = −84 = −2.
Put m = −2 and the point (2, 7) into y = mx + b: 7 = −2(2) + b.
Solve for b: 7 = −4 + b, so b = 11.
Write the equation: y = −2x + 11. Check the other point: −2(6) + 11 = −1. It works.
Answer: The line is y = −2x + 11 (slope −2, y-intercept 11).
Common mistakes
✗ MistakeIn y = 3x + 8, the slope is 8.
✓ InsteadThe slope is 3 (the number multiplying x) and the y-intercept is 8.
Students sometimes swap these two. The slope is always the coefficient of x; the constant term on its own is the y-intercept.
✗ MistakeIn y = 5x − 2, the y-intercept is 2.
✓ Insteady = 5x − 2 is y = 5x + (−2), so b = −2 and the line crosses at (0, −2).
The form is y = mx + b with a plus sign. Subtracting 2 means adding −2, so the sign belongs to b.
✗ MistakeIn 2y = 6x + 4, the slope is 6.
✓ InsteadDivide by 2 first: y = 3x + 2, so the slope is 3 and b = 2.
You can only read m and b when y is alone with a coefficient of 1.
✗ MistakeIn y = 7 − 4x, the slope is 7.
✓ InsteadReorder it: y = −4x + 7. The slope is −4.
Order does not change the equation. Find the term that contains x; its coefficient, sign included, is the slope.
Point-slope form, y − y1 = m(x − x1), uses any point on the line. Slope-intercept form uses the special point (0, b). For example, y − 3 = 2(x − 1) simplifies to y = 2x + 1.
Standard form is Ax + By = C, such as 3x + 2y = 10. It hides the slope; solve for y to get slope-intercept form, y = −32x + 5.
Quick check: 3 questions
Question 1 of 3
Which equation has slope 3 and y-intercept −5?
Show answer and explanation
Answer: A. In y = mx + b, put m = 3 and b = −5: y = 3x − 5. Choice B swaps slope and intercept, C drops the minus sign, and D swaps them and changes the signs.
Question 2 of 3
What is the slope of the line 4x + y = 6?
Show answer and explanation
Answer: C. Subtract 4x from both sides: y = −4x + 6, so m = −4. Choice A forgets the sign change when 4x moves across, and B and D use the constant, which is the y-intercept.
Question 3 of 3
A line crosses the y-axis at (0, 2) and rises 1 unit for every 3 units it moves right. What is its equation?
Show answer and explanation
Answer: B. Slope is rise over run, 13, and b = 2, so y = 13x + 2. Choice A uses run over rise, C swaps m and b, and D gives the wrong sign for b.
Slope-Intercept Form: frequently asked questions
Can every line be written in slope-intercept form?
No. Every non-vertical line can, but a vertical line such as x = 4 cannot. Its slope is undefined, so there is no number to use for m, and it never crosses the y-axis at one point (unless it is the y-axis itself). Horizontal lines are fine: y = 4 is y = 0x + 4.
How do you graph an equation in slope-intercept form?
Plot the y-intercept (0, b) first. Then use the slope as rise over run: for m = 23, go up 2 and right 3 and plot a second point. For a negative slope such as −23, go down 2 and right 3. Draw a straight line through the points and extend it in both directions.
What do m and b mean in a word problem?
b is the starting value, the amount when x = 0, such as a 25-dollar sign-up fee. m is the rate of change, such as 30 dollars per month. Together, y = 30x + 25 gives the total cost after x months. Units help: m is always output units per input unit.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 8.EE.B.6, CCSS 8.F.A.3
Cite this entry
Effortless Math Team. “Slope-Intercept Form.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/slope-intercept-form/
Flashcard
TermSlope-Intercept Formy = mx + b
DefinitionA line written as y = mx + b: m is the slope and b is the y-intercept. In y = 2x + 5, the slope is 2 and b = 5.
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