SOLUTION: let L be a line that is neither vertical nor horizontal and which does not pass through the origin. Show that L is the graph of (x/a) + (y/b) = 1, where a is the x-intercept and b

Algebra ->  Rational-functions -> SOLUTION: let L be a line that is neither vertical nor horizontal and which does not pass through the origin. Show that L is the graph of (x/a) + (y/b) = 1, where a is the x-intercept and b       Log On


   

Question 443259: let L be a line that is neither vertical nor horizontal and which does not pass through the origin. Show that L is the graph of (x/a) + (y/b) = 1, where a is the x-intercept and b is the y-intercept of L.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply both sides by ab:
ab%28%28x%2Fa%29+%2B+%28y%2Fb%29%29+=+1%29
bx+%2B+ay+=+ab
ay+=+ab-bx
ay+=+b%28a-x%29
y+=+b%281-x%2Fa%29
+y+=+%28-b%2Fa%29x+%2B+b
Then by slope-intercept, b is the y-intercept.
To solve for the x intercept, let y = 0.
0+=+%28-b%2Fa%29x+%2B+b
-b+=+%28-b%2Fa%29x
-b%28-a%2Fb%29+=+x
%28cross%28-b%29%2Across%28-1%29%2Aa%29%2F%28cross%28b%29%29+=+x
a+=+x
Then a is the x-intercept.