Question 58921: Find the equation of a line that goes through the y-intercept of 2x - 3y = 24 and the x-intercept of 5x + 6y = 30. Leave your answer in slope-intercept form.
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! Given equation is 2x - 3y = 24
To find the y inyercept we put x = 0,
==> -3y = 24 or y = -8{dividing by 3]
So the first point is (0, -8)
5x + 6y = 30
Replacing y by 0 we get,
5x = 30 or x = 6[dividing by 5]
So the second point is (5,0)
Equation of a line through 2 points (x1,y1) and (x2,y2) is (y-y1)/(x-x1)= (y2-y1)/(x2-x1)
Applying that for our points we get,
(y+8)/(x-0) = (0+8)/(6+0)
==> (y+8)/x = 8/6
==> (y+8)/x= 4/3
On simplification we get, 3y + 24 = 4x
Or 3y = 4x - 24
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