Tutoring math 10, you cover slope-point form.  It’s usually the most convenient  way to find the equation of a line.  The tutor gives an example.

Slope-point form is probably much more popular among university students than at high school. It’s a minimalistic way to arrive at the equation of a line. Consider the following example:

Example 1: Find the equation of the line passing through (-1,3) and (5,-2).

Solution: First, draw a diagram.

To find the equation of a line, we always need the slope. (See my article here for the method.) In linear equations, the slope is often referred to as m. We find it by using the formula

slope=m=(y₂-y₁)/(x₂-x₁)=(-2-3)/(5-(-1))=-5/6

The slope is found to be -5/6. We are ready to apply the slope-point equation:

y-y₀=m(x-x₀)

We adopt a known point on the line as (x₀,y₀); it could be either one. Let’s choose (-1,3). Then, we sub in its values for (x₀,y₀) as well as -5/6 in for m:

y-3=(-5/6)(x-(-1))

We tidy up the signs, to arrive at

y-3=(-5/6)(x+1)

There it is, our equation of the line passing through (-1,3) and (5,-2).

The slope-point method is very handy for finding the equation of a line:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.