SOLUTION: Find an equation of the line through the pair of points. Write the equation in the form Ax+By=C (4,0) and (-8,5)

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line through the pair of points. Write the equation in the form Ax+By=C (4,0) and (-8,5)      Log On


   

Question 320576: Find an equation of the line through the pair of points. Write the equation in the form Ax+By=C
(4,0) and (-8,5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=4 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=-8 and y%5B2%5D=5.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%285-0%29%2F%28-8-4%29 Plug in y%5B2%5D=5, y%5B1%5D=0, x%5B2%5D=-8, and x%5B1%5D=4


m=%285%29%2F%28-8-4%29 Subtract 0 from 5 to get 5


m=%285%29%2F%28-12%29 Subtract 4 from -8 to get -12


m=-5%2F12 Reduce


So the slope of the line that goes through the points and is m=-5%2F12


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-0=%28-5%2F12%29%28x-4%29 Plug in m=-5%2F12, x%5B1%5D=4, and y%5B1%5D=0


y-0=%28-5%2F12%29x%2B%28-5%2F12%29%28-4%29 Distribute


y-0=%28-5%2F12%29x%2B5%2F3 Multiply


y=%28-5%2F12%29x%2B5%2F3 Simplify


So the equation that goes through the points and is y=%28-5%2F12%29x%2B5%2F3


I'll let you convert that equation into standard form.