Enter two points, a point and slope, or a slope and y-intercept to get the slope intercept form equation (y = mx + b) of a line. Choose your input method, fill in the coordinates or values, and the calculator returns the slope (m), y-intercept (b), x-intercept, and the full line equation — plus a visual graph of the line.
Line Equation (y = mx + b)
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Slope (m)
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Y-Intercept (b)
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X-Intercept
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Slope intercept form is a way to express the equation of a straight line as y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). It's one of the most commonly used forms of a linear equation because it directly reveals the slope and y-intercept at a glance.
First, calculate the slope using m = (y2 − y1) / (x2 − x1). Then substitute the slope and one of the points into the equation y = mx + b to solve for b. Once you have both m and b, you can write the full equation in the form y = mx + b.
The slope m represents the steepness and direction of a line. It tells you how much y changes for every 1-unit increase in x. A positive slope means the line rises from left to right, a negative slope means it falls, a slope of 0 means the line is horizontal, and an undefined slope means the line is vertical.
No. Slope intercept form is y = mx + b, while standard form is Ax + By = C. You can convert between them algebraically — rearrange standard form by solving for y to get slope intercept form. The two forms represent the same line but present the information differently.
The x-intercept is the point where the line crosses the x-axis (i.e., where y = 0). Set y = 0 in the equation y = mx + b and solve for x: x = −b / m. This gives you the x-intercept, provided the slope m is not zero.
Starting from standard form Ax + By = C, subtract Ax from both sides to get By = −Ax + C, then divide everything by B to get y = (−A/B)x + (C/B). Now you can read the slope m = −A/B and y-intercept b = C/B directly.
A line inclined at exactly 45° to the horizontal has a slope of 1. This is because slope equals the tangent of the angle of inclination, and tan(45°) = 1. Such a line rises exactly as much as it runs, giving the equation y = x + b for some y-intercept b.
Slope intercept form is used widely in science, economics, and engineering to model linear relationships. Examples include calculating speed (distance vs. time), predicting costs (fixed cost + variable rate), analyzing trends in data, and building machine learning models where the slope and intercept define a linear regression line.