Question

Find the equation of a line that is perpendicular to y=3x-8 and intersects this line at its y intercept.

Answer 1

If the slope of one line is m, and you want the slope of a 2nd line which is perpendicular to the first, find it by taking the negative reciprocal of the slope, m, of the 1st line.

You are given y=3x-8. What's the slope of this line?

What's the negative of this slope?

What's the negative reciprocal of this slope? Your answer is the slope of the new (perpendicular) line.

Answer 2

mathmale was helping.
the first step is to find the slope of your equation
y=3x-8

Do you know the slope ?

Answer 3

no i don't know the slope, I think thats whats confusing me the most.

Answer 4

oh, I'm thinking you were supposed to have learned it by now.
but if you see
y = m x + b
where m and b are numbers
(notice this matches your equation)
the number in front of the x (it's "name" is m) is the slope
and the "b" is the y-intercept

in your equation, :
y=3x-8
what is the slope ? i.e. what is the number in front of the x ?

Answer 5

oh ok so the slope is 3 and the y intercept is -8.

Answer 6

yes. that is good.

Here is a graph of this line (notice it goes through the y-axis at x=0, y=-8)
and it goes over 1 step and up 3 steps (that is what a slope of 3 means)

Answer 7

They want a line that is perpendicular. As math male was saying
the slope of a line that is perpendicular (makes a right angle)
is found by

1. "flipping" the slope
2. multiplying by -1

examples: slope is ½ , perpendicular slope is 2/1 * -1 or 2*-1 or -2
or -2 : think of it as -2/1 , now flip it,1/-2 or - ½ , now multiply by -1 to get ½


what is 3 when you flip it, and multiply by -1 ?

Answer 8

-1/3

Answer 9

so the perpendicular line, starting with the "generic" equation
y= mx + b
we know m is -⅓

\[ y= -\frac{1}{3} x+b\]
we know the point (0,-8) is supposed to be on this line
(because they tell us intersects this line at its y intercept i.e. at (0,-8)
so put in 0 for x and -8 for y

Answer 10

you should get this:
\[ -8= -\frac{1}{3}\cdot 0 + b\]
now simplify the right side

Answer 11

what is -⅓ * 0 ?

Answer 12

0

Answer 13

so now you have
-8= 0+b
what is 0+b simplify to?

Answer 14

adding 0 to something does not change it.
0+1= 1
0+2= 2
0+b = b

Answer 15

so now its -8=b

Answer 16

which means b is -8
so we put in -8 for b in the equation
\[ y= -\frac{1}{3} x+b\]

Answer 17

Ohh ok thank u so much this makes so much more sense now.

Answer 18

you should get
\[ y= -\frac{1}{3}x-8\]
Here is what the lines look like.

Answer 19

Now i get it thank u for helping me.