# [MOVED] perpendicular line...what is k?

#### yaong

##### New member
The equation of the line m is 8x - 14y + 3 = 0

a) For what value of k is the graph of kx - 7y + 10 = 0 parallel to line m?

My work:

. . .slope:
. . . . .-A/B = -8/-12 = 8/12 = 4/7
. . . . .-A/B = -?/-7
. . . . .k = 4

b) What is k if the graphs of m and kx - 7y + 10 = 0 are perpendicular?

I don't know how to do this part.

The answer to part b is -49/4, but I have no idea how to get the answer. I thought all you had to do was find the opposite reciprocal but it turns out to be -7/4 NOT -49/4

#### galactus

##### Super Moderator
Staff member
Solve m for y:

$$\displaystyle \L\\y=\frac{4x}{7}+\frac{3}{14}$$

The other equation is:

$$\displaystyle \L\\y=\frac{kx}{7}+\frac{10}{7}$$

Since they are parallel, the slopes are the same. in the latter equation, what value of k makes the slope 4/7? .

If they are perpendicular, the slope of the k equation is the negative reciprocal of the m equation.

$$\displaystyle \L\\\frac{kx}{7}+\frac{10}{7}$$

What value of k makes the slope -7/4?.

$$\displaystyle \frac{k}{7}=\frac{-7}{4}$$

Solve for k.

#### pka

##### Elite Member
Here is another way to look at it:
The line $$\displaystyle Ax + By + C = 0$$ has slope $$\displaystyle \frac{{ - A}}{B}$$ if $$\displaystyle AB \not= 0$$.
Lines with the same slope are parallel.
Lines who’s slopes multiple to $$\displaystyle - 1$$ are perpendicular.
So line $$\displaystyle Ax + By + C = 0$$ is perpendicular to line $$\displaystyle Bx -Ay + C = 0.$$