How do you find the equation of the line that goes through (-3, 1) and (1, -3)?

1 Answer
Oct 4, 2017

Equation: x+y+2=0

Explanation:

The two point are (-3, 1) and (1, -3).

You can find the equation by using the point-gradient formula, y-y_1=m(x-x_1).

To do this, we first need to find the gradient of the line. This can be done using the gradient formula:

(y_1-y_2)/(x_1-x_2)
= (1-(-3))/(-3-1)
=4/-4
=-1

We now have the gradient, represented by m in the point-gradient formula, and can choose any one of the two coordinates given by the question to sub into this formula. Let's go with (-3, 1).

y-y_1=m(x-x_1)
y-1=-1(x-(-3))
y-1=-1(x+3))
y-1=-x-3
therefore y=-x-2

Or, if the question asks for the equation in general form, move all the values to one side so that the coefficient of x is positive and the equation equals to 0:
y=-x-2
therefore x+y+2=0