Math · Interactive
Slope-Intercept Form
Every linear equation y = mx + b draws a straight line. Drag the slope m and the y-intercept b below to reshape it and watch the slope, intercepts, and direction update live. Free to use, and exportable into your slides.
Drag the m and b sliders to reshape the line. Open fullscreen ↗
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What is slope-intercept form?
Slope-intercept form is the equation of a straight line written as y = mx + b. The letter m is the slope, which measures how steep the line is, and b is the y-intercept, the y-value where the line crosses the vertical axis. Because both the steepness and the starting height are visible directly in the equation, slope-intercept form is the fastest way to graph a line by hand. Drag the m and b sliders in the grapher above to see each part change the line.
What the slope m tells you
The slope m is the rise over the run: how many units the line goes up (or down) for every one unit it moves to the right. A positive slope rises from left to right, a negative slope falls, a slope of zero is a flat horizontal line, and a larger absolute value makes a steeper line. The dashed triangle in the grapher shows one unit of run and the matching rise so you can read the slope straight off the picture.
How to graph a line from y = mx + b
Start by plotting the y-intercept b as the point (0, b) on the vertical axis. From there, use the slope as rise over run: count up by the rise and right by the run to plot a second point, then draw the line through both. For example, for y = 2x - 3 you plot (0, -3), then go up 2 and right 1 to reach (1, -1), and connect them.
Finding the x-intercept and direction
The x-intercept is where the line crosses the horizontal axis, found by setting y = 0 and solving x = -b / m. A line with a positive slope is increasing, a negative slope is decreasing, and a slope of zero is constant. The panel in the grapher reports the slope, both intercepts, and the direction as you drag, connecting the equation to the graph.
Frequently asked questions
What is slope-intercept form?
Slope-intercept form is a linear equation written as y = mx + b, where m is the slope and b is the y-intercept. It makes graphing a line quick because both values are read directly from the equation.
What do m and b stand for in y = mx + b?
m is the slope, the rise over the run that sets how steep and in which direction the line goes. b is the y-intercept, the y-value where the line crosses the vertical axis, i.e. the point (0, b).
How do you graph a line in slope-intercept form?
Plot the y-intercept (0, b) first, then use the slope as rise over run to step to a second point, and draw the line through them. The interactive above does this automatically as you drag m and b.
How do you find the x-intercept from slope-intercept form?
Set y = 0 and solve for x, which gives x = -b / m. That point (−b/m, 0) is where the line crosses the horizontal axis, as long as the slope m is not zero.
What does a negative slope mean?
A negative slope means the line falls from left to right: as x increases, y decreases. A positive slope rises, and a slope of zero is a flat horizontal line.
How do I use this slope-intercept grapher?
Drag the m and b sliders to change the line. The graph redraws instantly and the panel shows the slope, y-intercept, x-intercept, and direction. You can also export the graph to use in your own slides.