Exercises: Finding line equations

You are given the points $P(1|3)$ and $Q(3|-1)$.

You are looking for the equation of the straight line that passes through the two points.

To determine the linear equation, it is best to first consider the general form of the linear equation:

Firstly, recall the equation for the gradient of a straight line:

Plug the values $x_1,x_2,y_1,y_2$ from the points $P$ and $Q$ into the formula.

$m=\frac{-1-3}{3-1}=\frac{-4}{2}$

Shorten the denominator.

$m=-2$

Now you know that the equation of the line through the points $P$ and $Q$ looks like this:

Next, determine the y -intercept ($t$).

To determine $t$, insert the $x$- and $y$-values of one of the two points into the equation of the line. This is calculated using the point $P$ as an example

$3=-2\cdot 1+t$

$3=-2+t$

$t=5$

The $y$-intercept of the function is 5. This gives you the function equation.

$y=-2\cdot x+5$