How do you find the equation of the line which has a y-intercept of 13 and is parallel to the line joining the points (8, 12) and (-9, 10)?

1 Answer
Alan P.
Jun 28, 2016

#2x-17y=-221#

Explanation:

A line with a y-intercept of 13 passes through the point #(0,13)# (by definition of y-intercept)

A line parallel to the line joining the points #(8,12)# and #(-9,10)#
has the same slope as the line joining #(8,12)# and #(-9,10)#, namely
#color(white)("XXX")m=(Deltay)/(Deltax)=(12-10)/(8-(-9))=2/17#

Using the point-slope form:
#color(white)("XXX")y-13=2/17(x-0)#

#color(white)("XXX")17y-17xx13=2x#

#color(white)("XXX")2x-17y = -221#

graph{(2x-17y+221)((x-8)^2+(y-12)^2-0.1)((x+9)^2+(y-10)^2-0.1)=0 [-14.63, 17.4, 5.02, 21.04]}

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