11.3 Finding the equation of a line — Learn

Prerequisites: identify gradient and vertical intercept in $y=mx+c$.

Objectives

By the end of this section, you can find the equation of a line through two points or through one point with a given gradient.

Find an equation from a point and gradient

A straight-line equation has the form $y=mx+c$. If you know the gradient $m$ and one point $(x,y)$, substitute them into the equation to find $c$.

Worked example. Find the line through $(2,1)$ with gradient 3.

Check: when $x=2$, $y=3(2)-5=1$.

To find a line through two points, first calculate the gradient, then substitute one point to find $c$.

Watch out. The vertical intercept is not the $y$-coordinate of every point. Substitute the known point into $y=mx+c$ before stating $c$.

Progress check

The station walk starts at distance 0, so $c=0$. With gradient $1/15$ km per minute, its model is $d=t/15$.

You should now be able to

• find the equation of a line through two points or through one point with a given gradient.;
• check your result by substitution or by interpreting the graph;
• explain the method in your own words.