Question

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)?

Answer 1

`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]}