SOLUTION: write an equation of the line that passes through the point (4,4) and is perpendicular to the line whose equation is 2x + y = 7

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Question 192965: write an equation of the line that passes through the point (4,4) and is perpendicular to the line whose equation is 2x + y = 7
Found 2 solutions by yuendatlo, jojo14344:
Answer by yuendatlo(23) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++

Any system of equations:


has solution

or



(x=1, y=1}

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given Line: 2x%2By=7red%28EQN1%29 ---> y=highlight%28-2%29x%2B7, where,
Slope=m=-2
Therefore, the line passing thru (4,4) that is perpendicular has a Slope, m%5B2%5D=-1%2Fm=-1%2F-2=red%281%2F2%29.

But remember the intercepts of red%28EQN1%29:
Let Fy=0:
2x%2B0=7 ---> cross%282%29x%2Fcross%282%29=7%2F2
red%28x=7%2F2%29, or (3.5,0), X-Intercept of red%28EQN1%29
Let Fx=0:
2%280%29%2By=7
red%28y=7%29, Y-Intercept of red%28EQN1%29


On red%28EQN2%29:
Thru point (4,4),
y=mx%2Bb
4=%281%2Fcross%282%29%29%28cross%284%292%29%2Bb
b=4-2=2, Y-Intercept

It follows, red%28y=%281%2F2%29x%2B2%29 red%28EQN2%29(Answer)--> Line passing thru (4,4)

Let Fy=0:
0=%281%2F2%29x%2B2
-2=%281%2F2%29x
x=2%2A-2=-4, X-Intercept

We see the line;
----> red%28RED=EQN1%29; green%28GREEN=EQN2%29

Thank you,
Jojo