Math
Slope-Intercept Form Calculator
Find the slope-intercept form y = mx + b from two points or from a slope and a point. Also returns standard and point-slope forms.
Choose an input mode
Point 1 (x1, y1)
Point 2 (x2, y2)
Equation
y = 2x + 1
Slope (m)
2
y-intercept (b)
1
x-intercept
-0.5
Point-slope form
y - 3 = 2(x - 1)
Standard form
2x - y = -1
Frequently Asked Questions about the Slope-Intercept Form Calculator
What is slope-intercept form?
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the y-value where the line crosses the y-axis). For example, y = 2x + 3 has a slope of 2 and crosses the y-axis at (0, 3). Any non-vertical line can be written this way.
How do you find y = mx + b from two points?
First calculate the slope: m = (y2 - y1) / (x2 - x1). Then find the y-intercept using b = y1 - m * x1 with either point. For example, from (1, 5) and (3, 11): m = (11 - 5) / (3 - 1) = 3, then b = 5 - 3 * 1 = 2, giving y = 3x + 2.
How do you find the equation from a slope and one point?
Plug the slope m and the point (x1, y1) into b = y1 - m * x1. That gives you the y-intercept, and the equation is y = mx + b. The calculator also outputs the point-slope form y - y1 = m(x - x1), which uses the same inputs without an intermediate step.
What happens when the two points form a vertical line?
If both points share the same x-value, the slope is undefined and y = mx + b cannot represent the line. The calculator returns x = c, where c is that shared x-value, the only correct form for a vertical line.
How do you convert y = mx + b to standard form?
Standard form is Ax + By = C with integer coefficients and A > 0. Starting from y = mx + b, rearrange to mx - y = -b. If m is a fraction, multiply every term by the denominator to clear it, then divide through by the GCD of all three coefficients to reduce to lowest terms. The calculator handles this automatically.