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Slope-Intercept Form Calculator

Find the y-intercept and write the slope-intercept equation of a line.

How it is calculated

The line y = m·x + b must pass through your point, so putting the point in and solving for the intercept gives b = y − m × x. Here m is the slope you enter and (x, y) is the known point. The tool shows b first and the slope m second (unchanged from your input), both with four decimals; you then write the equation as y = mx + b yourself. Every slope is accepted, including 0 (a horizontal line, where b equals the point's y) and negative values. Vertical lines have no slope and cannot be entered. If the point already lies on the y-axis (x = 0), b is simply y.

Worked example

A taxi charges 3.5 per kilometre, and a 10 km trip cost 50 in total. Treat the cost as a line with slope 3.5 passing through the point (10, 50). Step 1: m × x = 3.5 × 10 = 35. Step 2: b = 50 − 35 = 15. The tool prints a y-intercept of 15.0000 and a slope of 3.5000, so the cost line is y = 3.5x + 15, meaning a fixed starting charge of 15.

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Common mistakes

  • Adding instead of subtracting. The formula is b = y − m·x; using y + m·x gives 85 here instead of 15.
  • Swapping the point's x and y values, which gives a completely different intercept.
  • Entering the intercept of a different line in the slope field. Only the rate of change belongs there.
  • Dropping a minus sign on a negative slope. With m = −2 and the point (3, 8), b = 8 − (−6) = 14, not 2.
  • Writing the final equation as y = bx + m, with the two numbers the wrong way round. The slope multiplies x.

About this calculator

The slope-intercept form of a line, y = mx + b, expresses a linear equation in terms of its slope m (the rate of change, or “rise over run”) and its y-intercept b (where the line crosses the vertical axis). Given a slope and any single point on the line, b is found by rearranging the equation, since that point must satisfy it.

This form is one of the most commonly used ways to represent linear relationships because m and b can be read directly from a graph or a real-world scenario — for example, in a cost equation, m represents the per-unit cost and b represents a fixed starting cost — making it standard in algebra courses, linear regression trend lines, and any application that models a straight-line relationship between two variables.

This calculator takes a slope and one point on the line and returns the y-intercept (rounded to four decimals) along with your slope repeated for reference. Put the two values into y = mx + b to write the complete equation.

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