Slope-Intercept Form (y = mx + b): How to Find and Graph It
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This guide shows how to find the equation from a graph, two points, or a point and slope, graph it, and convert standard form.
Slope-intercept form is
y = mx + b, wheremis the slope of the line andbis the y-intercept, the y-value where the line crosses the vertical axis. Read the equation directly: the number multiplyingxis the slope, and the lone number is where the line starts on the y-axis.
If you have two points and just want the equation, our slope calculator returns the slope, the y-intercept, and the full y = mx + b line instantly. Everything below explains how to read, find, and graph that equation by hand.
What do m and b mean in y = mx + b?
The two letters are the only things you need to identify, and each controls one feature of the line. m is the slope and b is the y-intercept. The slope sets the tilt, how steep the line is and which way it leans. The y-intercept sets the starting height, where the line crosses the y-axis when x is zero.
The most common mix-up is swapping the two. The number stuck to the x is always the slope; the number standing alone is always the intercept. So in one example the slope is the coefficient and the intercept is the constant, and reading them off takes no work once the equation is in this form.
How do you find slope-intercept form from a graph?
Reading a line off a graph is the quickest case, because the intercept is sitting right there. Find b where the line crosses the y-axis, then count rise over run to get m. Look at where the line cuts the vertical axis for the intercept, then pick a second clean grid point and count how far up and how far across you travel between the two.
crosses y-axis at y = 1 → b = 1 from (0, 1) to (2, 5) rise = 5 − 1 = 4 run = 2 − 0 = 2 m = rise ÷ run = 4 ÷ 2 = 2 equation = y = 2x + 1
If counting the squares feels fiddly, lock in any two points on the line and let the rise-over-run slope formula do the arithmetic for the slope first.
How do you find slope-intercept form from two points?
Two points need one extra step, because neither one is necessarily the intercept. Find the slope first, then plug one point back in to solve for b. Use the slope formula to get m, substitute that slope and either point into y = mx + b, and solve the resulting equation for b. Both points give the same b, so pick whichever has friendlier numbers.
Checking with the other point confirms it. Substitute the second point into the finished equation; if both sides match, the line is right.
When you want the slope, intercept, and equation done for you from any two points, the slope calculator does all three at once.
How do you find the equation from a point and a slope?
This is the easiest case, because the slope is already handed to you. Substitute the known slope and the point into y = mx + b, then solve for b. With m already known, only the intercept is unknown, so one substitution finishes the job.
If you would rather skip solving for b, point-slope form, y − y₁ = m(x − x₁), holds the same information and rearranges into slope-intercept form with a little distributing.
How do you graph a line in slope-intercept form?
The form is built for graphing, so the steps fall straight out of it. Plot b on the y-axis, then use the slope as rise over run to step to the next point. Start at the intercept, treat the slope as a fraction of rise over run, count up the rise and across the run to land a second point, then draw the line through both.
start at b = (0, 1)
slope m = 2 = 2/1 (up 2, right 1)
next point = (1, 3)
again = (2, 5)
draw line through the pointsA negative slope just means you step down instead of up as you move right, and a fractional slope like one-half means up one for every two across.
How do you convert standard form to slope-intercept form?
Standard form, Ax + By = C, hides the slope and intercept until you rearrange it. Solve for y, and the equation lands in slope-intercept form. Move the x term to the right side, then divide every term by the coefficient on y. Whatever ends up multiplying x is the slope, and the constant is the intercept.
Going the other direction, from y = mx + b back to standard form, you clear any fractions and move both variable terms to the left.
How do you find the x- and y-intercepts?
Slope-intercept form already shows one intercept and makes the other a quick substitution. The y-intercept is b; for the x-intercept, set y to zero and solve for x. A line crosses the y-axis where x is zero, which is exactly the b term. It crosses the x-axis where y is zero, so set the equation equal to zero and solve.
For lines you meet later, like parabolas from the quadratic formula, finding where the curve crosses an axis works the same way: set the other variable to zero and solve.
To pin down a line in slope-intercept form: the slope m is the tilt and the intercept b is where it crosses the y-axis. Read them straight off y = mx + b, find the slope first when you start from points, and plot from b using rise over run to graph it. When you want the slope, intercept, and equation from two points worked out instantly, use the slope calculator.
Common questions
It is y = mx + b, the equation of a straight line written so the slope and y-intercept are visible. The m is the slope and the b is the y-intercept, the point where the line crosses the vertical axis.
b is the y-intercept, the y-value where the line crosses the y-axis. It is the height of the line when x equals zero, so the line always passes through the point (0, b).
Substitute the slope for m and the point's coordinates for x and y in y = mx + b, then solve for b.
Yes. Some countries write the constant as c instead of b, but it means the same thing: the y-intercept. The letters are just labels, so y = mx + c is identical slope-intercept form.
A horizontal line has slope zero, so the mx term disappears and the equation is just y = b. Every point on the line shares the same y-value, which is the intercept.
