Slope Intercept Form Calculator

What this calculator does

So, you want the equation of a line written in slope-intercept form, the familiar y = mx + b. This tool builds it for you, and it is flexible about what you start from: two points on the line, a point and the slope, or the slope and the y-intercept.

A dropdown picks which of those three you have, and the input boxes change to match.

How to use it

1. Choose your known information: two points, one point and the slope, or the y-intercept and the slope.
2. Enter the values for that choice.
3. Press Calculate.

When you start from two points, the tool works out the slope itself first, reducing it to a tidy fraction, then assembles the equation.

The form: y = mx + b

Slope-intercept form writes a line as

y = mx + b

where m is the slope and b is the y-intercept. It is the form most people meet first and reach for most often, because it reads almost like instructions for drawing the line: start at the height b on the y-axis, then climb by the slope m for every step across. Two numbers, and the whole line is pinned down.

What m and b tell you

The two letters each carry one clear fact. The slope m is the steepness, the rise over run, how sharply the line climbs or falls. The intercept b is where the line crosses the y-axis, its height at x = 0, the starting point. Change m and you tilt the line; change b and you slide it up or down without changing its tilt. Because both facts sit right there in the equation, slope-intercept form is the easiest to graph and the easiest to read at a glance.

The three ways to give it a line

A line can be described by different scraps of information, and the tool accepts the three most common. From two points, it finds the slope from the rise over the run, then uses one point to find b. From a point and the slope, it already has m and only needs to work out b so the line passes through your point. From the slope and the y-intercept, it has both m and b already, so it simply writes them into the form. Whichever you pick, the answer is the same line in the same y = mx + b shape.

A worked example, step by step

Take the two points (1, 3) and (3, 7).

• Slope: rise over run = (7 - 3) / (3 - 1) = 4 / 2 = 2, so m = 2.
• Find b using (1, 3): 3 = 2 times 1 + b, so b = 1.
• The equation is y = 2x + 1.

The line climbs 2 for every step across and crosses the y-axis at height 1.

Vertical lines

A vertical line cannot be written in slope-intercept form, because it has no slope to put in place of m. When two points share an x-value, the line is vertical, and the tool describes it instead by the equation x = a fixed value, which is the honest way to write a straight up-and-down line.

Questions people ask

What are m and b?

m is the slope, the steepness of the line, and b is the y-intercept, the height where the line crosses the y-axis at x = 0.

What can I start from?

Any of three: two points on the line, one point together with the slope, or the slope together with the y-intercept.

Why is this form so useful for graphing?

Because it reads like drawing instructions: begin at b on the y-axis, then rise by m for each step to the right, and the line takes shape.

Can it handle a vertical line?

A vertical line has no slope, so it cannot be written as y = mx + b. The tool gives it as x equals a fixed value instead.

What if I want other forms of the equation?

The point-slope form calculator writes it as y - y1 = m(x - x1), and the equation of a line calculator gives all three forms, including standard form, at once.

References

On slope-intercept form. A line can be written as y = mx + b, with m its slope and b its y-intercept, one of the standard ways to express a line in the coordinate plane.

1. Eric W. Weisstein, "Slope-Intercept Form," from MathWorld, a Wolfram resource, on y = mx + b, where b is the y-intercept and m is the slope.
2. Christopher Stover and Eric W. Weisstein, "Line," from MathWorld, a Wolfram resource, on the line and its several standard forms.