# Thread: Someone help? Equation/perpendicular/parallel lines

1. ## Someone help? Equation/perpendicular/parallel lines

I don't understand. I looked at how to do it and used their same method, but I didn't arrive at the same answer as the one provided in the back of the book.

The question is:

Find equations of lines that pass through the point (3,8) and are (a) parallel to and (b) perpendicular to -4x+7y=-5.

The answer in the back of the book for this chapter test question is $\displaystyle 4x-7y+44 = 0.$

$\displaystyle y-8 = \frac{4}{7}(x-3)$

$\displaystyle 7(y-8)= 4(x-3)$

$\displaystyle 7y+56 = 4x-12$

$\displaystyle \frac{7y}{7}= \frac{4x}{7}-\frac{44}{7}$

$\displaystyle y = \frac{4}{7}x-\frac{44}{7}$

OK, originally I messed up with the arithmetic, ugh. But I think I know how, am I right

You multiply the denominator and get 7y =4x-44 and move all the terms on one side...

4x-7y+44 = 0.

$\displaystyle 7(y-8)=4x-12$

$\displaystyle 7y\textcolor{red}{-}56=4x-12\Rightarrow 4x-7y+44=0$

b) The slope of the perpendicular line is $\displaystyle -\frac{7}{4}$

3. Originally Posted by A Beautiful Mind
I don't understand. I looked at how to do it and used their same method, but I didn't arrive at the same answer as the one provided in the back of the book.

The question is:

Find equations of lines that pass through the point (3,8) and are (a) parallel to and (b) perpendicular to -4x+7y=-5.

The answer in the back of the book for this chapter test question is $\displaystyle 4x-7y+44 = 0.$
There are two questions here, (a) and (b). Which one are you talking about?

$\displaystyle y-8 = \frac{4}{7}(x-3)$
Okay, the slope of the equation -4x+ 7y= -5, which is the same as 7y= 4x- 5 or y= (4/7)x- 5/7 is 4/7 and so a line through (3, 8) is y- 8= (4/7)(x- 3)
You are solving (a)?

$\displaystyle 7(y-8)= 4(x-3)$

$\displaystyle 7y+56 = 4x-12$
Sign error: 7(y- 8)= 7y- 56, not 7y+ 56.

$\displaystyle \frac{7y}{7}= \frac{4x}{7}-\frac{44}{7}$
Why divide? The solution in the back of the book, that you apparently are trying to duplicate, has no fractions. Just subtract 7y from both sides and add 12 to both sides: -56+12= -44= 4x+ 7y so 4x+7y+ 44= 0.

$\displaystyle y = \frac{4}{7}x-\frac{44}{7}$

OK, originally I messed up with the arithmetic, ugh. But I think I know how, am I right

You multiply the denominator and get 7y =4x-44 and move all the terms on one side...

4x-7y+44 = 0.
But what about (b)? A line perpendicular to a line with slope 4/7 has slope -7/4 (so the product is -1). The equation of a line through (3, 8) with slope -7/4 is y- 8= (-7/4)(x- 3). Multiply on both sides by 4 to get 4(y- 8)= -7(x- 3). Multiply that out and simplify.