What is the equation of the line passing through #(2,-8)# and #(5,-3)#?

1 Answer
Meave60
Nov 30, 2015

The equation in slope intercept form is #y=5/3x-34/3#.

Explanation:

First find the slope, #m#.

#m=(y_2-y_1)/(x_2-x_1)#

#(x_1,y_1)=(2,-8)#

#(x_2,y_2)=(5,-3)#

#m=(-3-(-8))/(5-2)#

#m=(-3+8)/3#

#m=5/3#

Us the point slope form of a linear equation, #y-y_1=m(x-x_1)#, where #m# is the slope and #(x_1,y_1)# is one of the points on the line, such as #(2,-8)#.

#y-y_1=5/3(x-x_1)#

#y-(-8)=5/3(x-2)#

#y+8=5/3(x-2)#

Multiply both sides times #3#.

#3(y+8)=5(x-2)#

#3y+24=5x-10#

Subtract #24# from both sides.

#3y=5x-10-24#

#3y=5x-34#

Divide both sides by #3#.

#y=5/3x-34/3#

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