Slope-Intercept Form

What m and b tell you

In $y = mx + b$, the slope $m$ is the number multiplying $x$, and $b$ is the constant on the end. The line crosses the $y$-axis at the point $(0, b)$ — substitute $x = 0$ and the $mx$ term vanishes, leaving $y = b$.

So $y = 2x + 1$ is a line that crosses the $y$-axis at $(0, 1)$ and rises $2$ for every $1$ step right. That is the line drawn below.

Reading m and b from an equation

For an equation already in the form $y = mx + b$, just read the two numbers: in $y = -3x + 4$, the slope is $m = -3$ and the $y$-intercept is $b = 4$. Keep the sign with the number it belongs to.

Two cases trip students up. When $x$ appears alone, as in $y = x - 5$, the coefficient is $1$, so $m = 1$ and $b = -5$. And when the terms come in the other order, as in $y = 7 - 3x$, rewrite it with the $x$-term first: $y = -3x + 7$, so $m = -3$ and $b = 7$ — the $7$ is not the slope just because it comes first.

Writing the equation from a graph

Work in two reads. First find $b$: look where the line crosses the $y$-axis. Then find $m$: starting from that crossing point, count the rise and run to the next clean grid point on the line.

Always start with the intercept — it anchors the line. If the line crosses at $(0, -3)$ and rises $1$ for every $2$ steps right, the equation is $y = \dfrac{1}{2}x - 3$.

Worked examples

Try one yourself

Common questions