What is the slope intercept form of the line passing through #(2,-3) # with a slope of #3/2 #?

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Answer 1 · 2015-12-13T18:18:02

#y=3/2x+13/2#

Given:

Point: #(2,-3)#

Slope: #3/2#

You can use the point-slope form: #y-y_0=m(x-x_0)#, where #m# is the slope and #(x_0,y_0)# is a point on the line.

Solution:

#[1]" "y-y_0=m(x-x_0)#

Substitute the point #(2,-3)# into #(x_0,y_0)#.

#[2]" "y-2=m(x+3)#

Substitute the slope #3/2# into #m#.

#[3]" "y-2=3/2(x+3)#

Isolate #y# so you can express the line in the slope-intercept form: #y=mx+b#

#[4]" "y=3/2(x+3)+2#

Multiply #3/2# to #(x+3)#.

#[5]" "y=3/2x+9/2+2#

#[6]" "y=3/2x+9/2+4/2#

#[7]" "color(blue)(y=3/2x+13/2)#