SOLUTION: write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the given line. Given: (-3,1); y=1/3x+2, (4,-3); 2x-7y=14

Algebra ->  College  -> Linear Algebra -> SOLUTION: write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the given line. Given: (-3,1); y=1/3x+2, (4,-3); 2x-7y=14       Log On


   



Question 999556: write an equation in slope intercept form of the line that passes through the given point and is perpendicular to the given line. Given: (-3,1); y=1/3x+2, (4,-3); 2x-7y=14

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
(4,-3); 2x-7y=14

Solve for y and adjust into slope intercept form.
-7y=-2x%2B14
y=%282%2F7%29x-2
Slope is 2%2F7.

Determine what is negative reciprocal of 2%2F7.
That would be -7%2F2, and this is the slope of the line PERPENDICULAR to the given 2x-7y=14.

Line to be found, if in slope-intercept form is y=-%287%2F2%29x%2Bb and you want to find b.
y%2B%287%2F2%29x=b
b=y%2B%287%2F2%29x
Use the point which this line must pass through.
b=%28-3%29%2B%287%2F2%294
b=-3%2B14
b=11
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Line sought, in slope-intercept form is highlight%28y=-%287%2F2%29x%2B11%29. THIS LINE is perpendicular to 2x-7y=14 and passes through the required point (4,-3).

Adjust the line into standard form, IF YOU WANT, since your given line was in standard form.
y=-%287%2F2%29x%2B11
2y=-7x%2B22
2y%2B7x=22
highlight%287x%2B2y=22%29

The two red-outlined equations are equivalent.