11.2 Gradient and intercept: y = mx + c — Learn

Prerequisites: read and plot coordinates, and divide integers.

Objectives

By the end of this section, you can calculate the gradient between two points and identify the gradient and vertical intercept in $y=mx+c$.

Gradient and intercept

The gradient measures the change in $y$ for each 1-unit increase in $x$. Calculate it by dividing the change in $y$ by the change in $x$.

In $y=mx+c$, $m$ is the gradient and $c$ is the vertical intercept, where the line crosses the $y$-axis.

Worked example. Find the gradient through $(1,2)$ and $(4,11)$.

The line rises 9 units while moving 3 units right, so its gradient is 3. In $y=-2x+5$, the gradient is $-2$ and the vertical intercept is 5.

Watch out. Keep the order consistent in both differences. If you calculate $11-2$ in the numerator, use $4-1$ in the denominator.

Progress check

The walker travels 2 km in 30 minutes. Its gradient is $2/30=1/15$ km per minute.

You should now be able to

• calculate the gradient between two points and identify the gradient and vertical intercept in $y=mx+c$.;
• check your result by substitution or by interpreting the graph;
• explain the method in your own words.