Slope-Intercept Form

What m and b tell you

In $y = mx + b$, the coefficient of $x$ is the slope $m$. In $y = 4x + 3$, the slope is $4$. In $y = -x + 6$, the slope is $-1$, because $-x$ means $-1 \cdot x$. If the slope came from two points, it's the value $\dfrac{y_2 - y_1}{x_2 - x_1}$.

The constant term is the $y$-intercept $b$ — the $y$-value where the line crosses the $y$-axis, at the point $(0, b)$. In $y = 4x + 3$, the line crosses at $(0, 3)$. If there is no constant written, as in $y = 5x$, then $b = 0$ and the line passes through the origin.

The graph below shows two lines with the same $y$-intercept, $b = 1$: the black line is $y = 2x + 1$ and the blue line is $y = -x + 1$. Both cross the $y$-axis at the same point, but the slopes send them in different directions — positive slope climbs to the right, negative slope falls.

Graphing a line from y = mx + b

Step 1: plot the $y$-intercept. Put a point at $(0, b)$ on the $y$-axis. That's the one point you get for free.

Step 2: use the slope to find a second point. Write $m$ as a fraction — the top is the vertical change, the bottom is the horizontal change. For $m = \dfrac{2}{3}$, move up $2$ and right $3$ from the intercept and plot a second point. For a negative slope like $m = -2 = \dfrac{-2}{1}$, move down $2$ and right $1$.

Step 3: draw the line through the two points. Two points determine the line — extend it in both directions with a straightedge.

Writing the equation from a graph

Go in reverse. First read $b$: find where the line crosses the $y$-axis. Then find $m$: pick two points where the line passes exactly through grid corners and compute $\dfrac{y_2 - y_1}{x_2 - x_1}$. Finally, drop both numbers into $y = mx + b$.

If the equation you're given isn't in slope-intercept form — something like $2x + y = 6$ — solve it for $y$ first. Subtracting $2x$ from both sides gives $y = -2x + 6$, and now the slope and intercept are visible.

Worked examples

Try one yourself

Common questions