parallell and perpendicular lines
posted by luckybee .
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(x7) +7
y2=3x+21+7
y=3x+28+2
y=3x+30
perpendicular line:
y2=1/3(x7) +7
y2=1/3x7/3 +21/3
y2==1/3x + 14
y=1/3x + 14 +2
y=1/3x +16

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(x7) + 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
y2 = (1/3)(x7)
then 3y  6 = x7
x  3y = 1 , the same result as mine