Comparing slopes through graphs

The slope of a line tells you two things at once: how steep it is, and whether it tilts up or down. A bigger size of slope means a steeper line. A line rising from left to right has a positive slope, and a line falling from left to right has a negative slope.

In the graph above, the steepest line is the one with slope $2$; the line with slope $0.5$ rises more gently; and the line with slope $-1$ falls, so its slope is negative.

To compare slopes on a graph, use steepness for the size and direction for the sign. A line rising more sharply has a larger positive slope, and a line falling more sharply has a more negative slope. And remember: any positive slope is greater than any negative slope.

You can read the actual slope as rise over run: how far the line goes up for each step to the right. A line that rises $2$ for every $1$ across has slope $2$.

Line P rises $3$ units for every $1$ unit across, and Line Q rises $1$ unit for every $1$ across. Which has the greater slope?
Line P rises more steeply, so its slope $3$ is greater than Line Q's slope $1$.

Line M goes up from left to right, and Line N goes down. Which has the greater slope?
Line M has a positive slope and Line N has a negative slope.
Any positive slope is greater than a negative one, so Line M has the greater slope.

A line rises $4$ units for every $2$ units across. What is its slope?
Slope is rise over run:
$\frac{4}{2} = 2$.