Find the equation of a straight line from two points on it

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Find the equation of the straight line passing through A(5, 21) and B(−3, −3), in the form y = mx + c.

Remember: Find the slope first. Then substitute one point into y = mx + c to find c.

The slope is ((−3) − 21) ÷ ((−3) − 5), which is (−24) ÷ (−8) = 3.
Substitute A: 21 = 3 × 5 + c, so c = 6.
The equation is y = 3x + 6.

Common mistakes

Found the intercept as y − x. It is y minus the slope times x.
The slope has the wrong sign.
The slope is upside down. It is the vertical change divided by the horizontal change.