What is the equation of the line between #(-1,12)# and #(7,-7)#?

1 Answer
Feb 27, 2016

The equation of the line that passes through the points #A(-1,12)# and #B(7,-7)# is :
#y = - 19/8 x + 77/8#

Explanation:

The standard form of the equation of a line is #y = m x + p# with m the slope of the line.

STEP 1 : Let's find the slope of the line.
# m = (y_B - y_A)/(x_B - x_A) = (-7-12)/(7+1) = - 19/8#
N.B : The fact that the slope is negative indicates the line decreases.

STEP 2 : Let's find p (coordinate at origin).
Use the point-slope formula with one of our points, e.g. #A(-1,12)# and #m = - 19/8#.

#12 = - 19/8 * -1 + p#
# p = 77/8#

Cross-check: Check the equation with the second point.
Use #B(7,-7)# in the equation :
#y = - 19/8 * 7 + 77/8 = - 96/8 + 77/8 = -56/8 = -7 #
-> Perfect !