Question

find the equation of the line through the given points (-5,20) and (1,2)

Answer 1

The general equation for a straight line is y=mx+a, where m is the slope.

Let's find the slope = (signed difference of y-coords)/(signed difference of x coords)=

(2-20)/(1-(-5))=-18/6=-3, so m=-3.

To find a we can simply substitute the coords for either point and solve for a:

let's use (1,2): 2=-3+a, a=5, so y=-3x+5.

Let's test this by plugging in x=-5: y=15+5=20, which means that (-5,20) is the other point, and so it is!