Slope Intercept Form Calculator (y = mx + b) With Steps

To use slope intercept form, solve the equation for y so it reads y = mx + b, where m is the slope and b is the y-intercept. For the points (2, 1) and (6, 7), the slope is m = 6/4 = 3/2, and putting (2, 1) into y = (3/2)x + b gives b = −2. The line is y = (3/2)x − 2.

How to use the slope intercept form calculator

1. Pick what you already know: two points, a slope and one point, a standard form equation Ax + By = C, a point-slope equation, or any other linear equation.
2. Enter whole numbers, decimals or fractions such as 3/4. For a vertical line, type “undefined” as the slope.
3. Or type the whole problem in the box at the top, for example 4x − 2y = 10 or (1, 2) and (3, 8). The calculator picks the right tab for you.
4. Read y = mx + b at the top, then open “Show steps” to follow the working. Standard form, point-slope form, a table of values and a graph come with every answer.

What m and b mean in y = mx + b

Slope-intercept form names the two numbers you need to draw a line. The slope m tells you how steep the line is: it is the rise (change in y) divided by the run (change in x). A positive m means the line climbs from left to right, a negative m means it falls, and m = 0 means it is flat.

The y-intercept b is where the line crosses the y-axis, at the point (0, b). Put x = 0 into y = mx + b and you get y = b, which is why the constant at the end is the intercept.

To graph y = (3/2)x − 2 by hand, plot (0, −2), then count up 3 and right 2 to reach (2, 1). Join the two points and extend the line. The graph in the calculator draws this rise and run as a dashed path.

Four ways to write an equation in slope-intercept form

From two points

Find the slope first, then use one point to find b. For (−3, 8) and (1, 0):

• m = (0 − 8)/(1 − (−3)) = −8/4 = −2
• Put (1, 0) into y = −2x + b: 0 = −2 + b, so b = 2
• Answer: y = −2x + 2. Check with (−3, 8): −2(−3) + 2 = 8.

From a slope and a point

Only b is missing, so substitute the point and solve. With m = 3/4 through (−4, 2): 2 = (3/4)(−4) + b, which is 2 = −3 + b, so b = 5. The line is y = (3/4)x + 5.

From standard form Ax + By = C

Get y alone in two moves: move the x-term to the right, then divide every term by B. For 4x − 2y = 10, subtract 4x to get −2y = −4x + 10, then divide by −2 to get y = 2x − 5. A shortcut is m = −A/B and b = C/B: here m = −4/(−2) = 2 and b = 10/(−2) = −5.

From point-slope form

Distribute the slope, then move the constant across. Starting with y + 3 = (1/2)(x − 4), distributing gives y + 3 = (1/2)x − 2. Subtract 3 from both sides: y = (1/2)x − 5.

Vertical and horizontal lines

A horizontal line has slope 0, so y = mx + b shrinks to y = b. The points (−1, 6) and (5, 6) give m = 0/6 = 0, and the line is y = 6.

A vertical line is the one case that has no slope-intercept form. For (4, −2) and (4, 5), the run is 4 − 4 = 0, and dividing by zero is undefined. Every point has x = 4, so the equation is x = 4. In standard form you can still write it as x + 0y = 4, which is why some textbooks prefer standard form for listing every line.

Converting y = mx + b back to standard and point-slope form

To go from y = −(3/4)x + 2 to standard form, multiply every term by 4 to clear the fraction: 4y = −3x + 8. Then add 3x to both sides: 3x + 4y = 8. The usual rules are integer A, B and C, a positive A, and no common factor.

For point-slope form you need any point on the line. When x = 4, y = −(3/4)(4) + 2 = −1, so the point (4, −1) gives y + 1 = −(3/4)(x − 4). The y-intercept works too: y − 2 = −(3/4)x.

Slope-intercept form quick reference

Common mistakes with slope-intercept form

• Flipping the slope. The change in y goes on top. Writing (x₂ − x₁)/(y₂ − y₁) gives the reciprocal, not the slope.
• Mixing the order of the points. If y₂ comes from the second point, x₂ must too. Subtracting in different orders flips the sign of m.
• Dividing only part of the equation by B. In 3x + 2y = 8 the constant must be divided as well: y = −(3/2)x + 4, not y = −(3/2)x + 8.
• Losing a sign with a negative B. Dividing by a negative number changes the sign of every term on the right.
• Reading b from the wrong form. In y − 4 = 2(x + 1) the 4 is not the y-intercept. Solve for y first: y = 2x + 6, so b = 6.

Where slope-intercept form shows up

Any quantity that starts at a fixed value and changes by the same amount each step fits y = mx + b. A plant that is 4 cm tall and grows 1.5 cm a week has height h = 1.5w + 4 after w weeks; after 6 weeks that is 13 cm. A gym that charges a 25-dollar sign-up fee plus 10 dollars a month costs C = 10n + 25 for n months. In both, b is the starting value and m is the rate of change, which is why this form is the one used for linear functions, trend lines and graphing.

Slope-intercept form practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

How do you find b in y = mx + b?

Put the slope and the coordinates of any point on the line into y = mx + b and solve for b. With slope 5 and the point (−2, −9): −9 = 5(−2) + b, so b = 1. If you know the point where x = 0, its y-coordinate is b directly.

Can every line be written in slope-intercept form?

Every line except a vertical one. A vertical line such as x = 6 has an undefined slope and never crosses the y-axis (unless it is the y-axis), so there is no m or b. Horizontal lines are fine: they have m = 0 and look like y = b.

How do you convert standard form to slope-intercept form?

Subtract the x-term from both sides, then divide every term by the coefficient of y. For 2x + 5y = −15: 5y = −2x − 15, so y = −(2/5)x − 3. The slope is −A/B = −2/5 and the y-intercept is C/B = −3.

What is the slope-intercept form of the x-axis?

The x-axis is the horizontal line through every point with y = 0, so m = 0 and b = 0, and its equation is y = 0. The y-axis is vertical (x = 0), so it has no slope-intercept form.

Can the slope or y-intercept be a fraction?

Yes. For (−2, 1) and (4, 5), m = 4/6 = 2/3 and b = 1 − (2/3)(−2) = 7/3, so y = (2/3)x + 7/3. The calculator keeps exact fractions like these instead of rounding them to decimals, and shows the decimal slope next to the fraction.

Related calculators

• Standard form calculator: convert y = mx + b to Ax + By = C, and write polynomials and numbers in standard form.
• Point-slope form calculator: write y − y₁ = m(x − x₁) from a point and a slope.
• Slope calculator: find the slope, distance and angle between two points.
• Equation of a line calculator: lines from intercepts and parallel or perpendicular lines, in every form.