Graphing Lines

Slope-intercept form and reading a line from its equation.

The idea

The graph of a linear equation in $x$ and $y$ is a straight line, and the form of the equation most convenient for graphing is slope-intercept form: $y = mx + b.$ The two constants $m$ and $b$ determine the line completely.

$b$ is the $y$-intercept, the height at which the line crosses the $y$-axis: setting $x = 0$ leaves $y = b$, so $(0, b)$ is on the line.

$m$ is the slope, the change in $y$ produced by increasing $x$ by $1$: raising $x$ by $1$ raises the term $mx$ by exactly $m$. A line with positive slope rises from left to right, a line with negative slope falls, and the larger $m$ is in absolute value, the steeper the line.

To draw the line, plot two points and join them. The $y$-intercept gives one, and substituting any other $x$ gives a second. To find where the line crosses the $x$-axis, set $y = 0$ and solve for $x$.

Ways to work on it

• Walkthrough. Slope-intercept form: the slope, a point on the line, and both intercepts.
• Practice. Read the slope, intercept, or a point from y = mx + b.
• Hardest. Convert standard form to slope-intercept form.

Not sure where to start? Take the ten-question placement test.