The formula this page uses
y = m x + b m = (y₂ − y₁) / (x₂ − x₁)
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Slope Intercept Form Calculator
Solve slope intercept form problems with clear steps, notation, and a final check.
Calculate without using AI.
Evaluate the governing formula locally in your browser. Define each known quantity once, then change values to test another case instantly.
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Algebra
Slope Intercept Form Calculator explained
The short version
- y = mx + b packs a whole line into two numbers: how steep it is, and where it crosses the y-axis.
- Slope is rise over run, so it is the change in y divided by the change in x, in that order.
- A vertical line has no slope-intercept form at all, because dividing by a run of zero is impossible.
What each part means
SymbolWhat it means
m — SlopeHow many units y moves for every 1 unit x moves right. In a word problem it carries a rate unit like dollars per hour.
b — y-interceptThe value of y when x = 0. In a word problem it is the starting amount.
(x₁, y₁) — First pointAny known point on the line.
(x₂, y₂) — Second pointA different known point. If x₂ = x₁ the line is vertical.
Show your work: a full example
- Two points on the line(−2, 7) and (4, −5)
- Change in y over change in xm = (−5 − 7) / (4 − (−2)) = −12 / 6
- Simplify the slopem = −2, so the line drops 2 for every 1 step right
- Put one point into y = mx + b7 = −2(−2) + b
- Simplify and solve for b7 = 4 + b, so b = 3
- Write the equationy = −2x + 3
- Check with the other point−2(4) + 3 = −8 + 3 = −5 ✓
A second, different case
- A different case: both points share an x(5, 1) and (5, 9)
- Try the slope formula(9 − 1) / (5 − 5) = 8 / 0, which is undefined
- So this line has no y = mx + b formwrite it as x = 5 instead
- A second branch: a perpendicular to y = −2x + 3 through (4, −5)flip and negate: m = −1 ÷ (−2) = 1/2
- Find its intercept−5 = ½(4) + b, so −5 = 2 + b
- Solveb = −7
- Write ity = ½x − 7, and ½ × (−2) = −1 confirms the two lines meet at a right angle
Copy-ready example
(−2, 7) and (4, −5)
Two points on the line
Questions about the Slope Intercept Form Calculator
What is the slope when both points have the same x?
It is undefined, not zero. The run is 0 and dividing by 0 has no answer, which matches the picture: a vertical line never gets anywhere sideways. Write x = 5 and skip y = mx + b entirely.
How do I turn y = mx + b into standard form?
Move the x term across and clear fractions. y = ½x − 7 becomes 2y = x − 14, then x − 2y = 14. Standard form is handy for systems of equations; slope-intercept form is handy for graphing.
Can two parallel lines ever be the same line?
If they share a slope and a y-intercept, they are one line drawn twice, and every point solves both equations. Genuinely parallel lines match on m but differ on b, so they never meet.
Does b have a unit in a word problem?
Yes, and it is usually the answer to 'how much at the start'. If y is dollars and x is hours, then b is dollars and m is dollars per hour, which is a fast way to check you assigned the two numbers correctly.