Posted by **luckybee** on Sunday, February 19, 2012 at 5:17pm.

please check my homework

given P(7,2) and the line y + 3x=7 find the equation for the line

parallel line: y+3x+7

y=-3(x-7) +7

y-2=-3x+21+7

y=-3x+28+2

y=-3x+30

perpendicular line:

y-2=1/3(x-7) +7

y-2=1/3x-7/3 +21/3

y-2==1/3x + 14

y=1/3x + 14 +2

y=1/3x +16

- parallell and perpendicular lines -
**Reiny**, Sunday, February 19, 2012 at 5:41pm
Here is a neat way to do these question in a quicker way

You should have learned that for a straight line equation in the form

Ax + By = C, the slope of the line is -A/B

so for 3x+y = 7 , a parallel line will differ only in the C value

so new equation is

3x + y = C

plug in the point (7,2)

21 + 2 = C = 23

so new equation: **3x + y = 23 or y = -3x - 23**

notice the given point does not even satisfy your final equation.

Your error is in the 2nd line, should be

y = -3(x-7) + 2

For the perpendicular short cut way:

slope of given equation is -3

so slope of perpendicular line is +1/3

new equation:

x - 3y = C, plug in the point (7,2)

7 - 6 = C = 1

**x - 3y = 1 or y = (1/3)x - 1/3**

again, you made the error in the 2nd line, it should say

y-2 = (1/3)(x-7)

then 3y - 6 = x-7

x - 3y = 1 , the same result as mine

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