SOLUTION: Please help me find the equation of the line that is perpendicular to the line 5x+2y=15 and has an x intercept of 5.

Algebra ->  Linear-equations -> SOLUTION: Please help me find the equation of the line that is perpendicular to the line 5x+2y=15 and has an x intercept of 5.      Log On


   

Question 1134593: Please help me find the equation of the line that is perpendicular to the line 5x+2y=15 and has an x intercept of 5.
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
find the equation of the line that is perpendicular to the line 5x%2B2y=15 and has an x+intercept of 5
given:
the line 5x%2B2y=15
x+intercept of 5=> it is a point (5,0)
if the line that is perpendicular to given line, and we know that perpendicular lines have slopes negative reciprocal to each other, we will find slope first
5x%2B2y=15...solve for y
2y=-5x%2B15
y=-%285%2F2%29x%2B15%2F2-> given line has a slope %28-5%2F2%29
=>so, perpendicular line will have a slope m=%28-1%29%2F%28-5%2F2%29=2%2F5
now use point slope formula to find equation:
y-y%5B1%5D=m%28x-x%5B1%5D%29.....plug in m=2%2F5 and coordinates of the point (5,0)

y-0=%282%2F5%29%28x-5%29
y=%282%2F5%29x-%282%2F5%295
y=%282%2F5%29x-%282%2Fcross%285%29%29cross%285%29
highlight%28y=%282%2F5%29x-2%29





Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite the line given as 2y=-5x+15
then divide by 2 for y=-(5/2)x+7.5, which is slope intercept form. The slope is -5/2.
Perpendicular lines have a negative reciprocal slope,meaning their slope product is -1. The slope of the line desired is +2/5
An x-intercept of (5, 0) is a point
point slope formula y-y1=m(x-x1) (x1, y1) point
y=(2/5)(x-5)
y=(2/5)x-2
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28-5%2F2%29x%2B7.5%2C%282%2F5%29x-2%29