What is the slope-intercept form of the line passing through #(4, 5)# and # (2, 2) #?

1 Answer
Feb 24, 2016

Answer:

#y = 3/2x - 2#
The equation for slope intercept is #y=mx+b#
For this equation the slope #m = 3/2#
and the y intercept is #b = -2#

Explanation:

The formula for slope is #m =(y_2 - y_1)/(x_2-x_1)#

For the points (4,5) and (2,2) where
#x_1 = 4#
#y_1 =5#
#x_2 = 2#
#y_2 = 2#

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

#m =(2 - 5)/(2-4)#

#m = (-3)/-2#

#m =3/2#

To determine the equation of the line we can use the point slope formula and plug in the values given in the question.

#(y - y_1) = m(x - x_1)#

#m = 3/2#
#x_1 = 4#
#y_1 = 4#

#(y - 4) = 3/2#(x - 4)#

#y - 4 = 3/2x - 6#

#y - 4 + 4 = 3/2x - 6 + 4 #

#y = 3/2x - 2#

The equation for slope intercept is #y=mx+b#

For this equation the slope #m = 3/2#
and the y intercept is #b = -2#