SOLUTION: Find a general linear equation ​(Ax+By+C=0, where​ A, B, and C are​ integers) of the straight line that has the indicated​ properties, and sketch the line. Passes throug

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Find a general linear equation ​(Ax+By+C=0, where​ A, B, and C are​ integers) of the straight line that has the indicated​ properties, and sketch the line. Passes throug      Log On


   

Question 1134566: Find a general linear equation ​(Ax+By+C=0, where​ A, B, and C are​ integers) of the straight line that has the indicated​ properties, and sketch the line.
Passes through(−4,5) and (3,8)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a general linear equation: ​Ax%2BBy%2BC=0
passes through (-4,5) and (3,8)

first use points to find a slope m
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%288-5%29%2F%283-%28-4%29%29
m=%288-5%29%2F%283%2B4%29
m=3%2F7

now use point slope form to find equation:

y-y%5B1%5D=m%28x-x%5B1%5D%29...plug in m and coordinates of the point (-4,5)
y-5=%283%2F7%29%28x-%28-4%29%29
y-5=%283%2F7%29%28x%2B4%29
y-5=3x%2F7%2B12%2F7............both sides multiply by 7
7y-35=3x%2B12
-3x%2B7y-35-12=0
-3x%2B7y-47=0