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

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Question 145656: Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7???
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2By=7 Start with the given equation.


y=-2%2Ax%2B7 Solve for y.


We can see that the equation y=-2%2Ax%2B7 has a slope m=-2 and a y-intercept b=7.


Now to find the slope of the perpendicular line, simply flip the slope m=-2 to get m=-1%2F2. Now change the sign to get m=1%2F2. So the perpendicular slope is m=1%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-4=%281%2F2%29%28x-4%29 Plug in m=1%2F2, x%5B1%5D=4, and y%5B1%5D=4


y-4=%281%2F2%29x%2B%281%2F2%29%28-4%29 Distribute


y-4=%281%2F2%29x-2 Multiply


y=%281%2F2%29x-2%2B4 Add 4 to both sides.


y=%281%2F2%29x%2B2 Combine like terms.


So the equation of the line perpendicular to 2x%2By=7 that goes through the point is y=%281%2F2%29x%2B2.


Here's a graph to visually verify our answer:
drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-2%2Ax%2B7%2C%281%2F2%29x%2B2%29%0D%0Acircle%284%2C4%2C0.08%29%2C%0D%0Acircle%284%2C4%2C0.10%29%2C%0D%0Acircle%284%2C4%2C0.12%29%29Graph of the original equation y=-2%2Ax%2B7 (red) and the perpendicular line y=%281%2F2%29x%2B2 (green) through the point .

Answer by edjones(7311) About Me  (Show Source):
You can put this solution on YOUR website!
2x+y=7
y=-2x+7 slop-intercept form
the slope (m) is -2.
The slope of a line perpendicular to this line is the negative reciprocal of its slope: 1/2 or .5
y-y[1]=m(x-x[1]) point-slope form
y-4=.5(x-4)
y-4=.5x-2
y=.5x+2 Answer
.
Below is a graph of the 2 equations. The green line is y=.5x-2. Note that it goes through the point (4,4)
.
Ed
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graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-2x%2B7%2C.5x%2B2%29