Exercises: Finding line equations

You are given the points $P(0|3)$ and $Q(2|-3)$

Insert the x-values (first coordinate) and the y-values (second coordinate) into the general line equation.

$3=m\cdot 0+t$

$-3=m\cdot 2+t$

In the first equation, you can immediately see that $t=3$ . You can insert this $t$ into the second equation to calculate $m$.

Plug $m$ and $t$ into the general line equation.

$y=-3x+3$

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

Calculate the difference between the two x-values and the two y-values to determine the gradient.

x-values: $3-1=2$

y-values: $-1-3=-4$

While the x-value increases by 2, the y-value decreases by 4. Divide the y-value by the x-value to calculate the gradient.

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

Substitute m, the x-value and the y-value of one of the points into the general line equation to determine $t$.

Plug $m$ and $t$ into the general linear equation to set up the equation of the function.

$y=-2x+5$