Question

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

Answer 1

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: <b>3x + y = 23 or y = -3x - 23</b>

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
<b>x - 3y = 1 or y = (1/3)x - 1/3</b>

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