Question

Choose the point-slope form of the equation below that represents the line that passes through the points (-6, 4) and (2, 0).

y - 4 = -1/2 (x + 6)
y - 4 = 2(x + 6)
y + 6 = - 1/2 (x - 4)
y + 6 = 2(x - 4)

Answer 1

first, find the slope of the line connecting \((x_1,y_1) = (-6,4)\) and \((x_2,y_2) = (2,0)\)
\[m = \frac{y_2-y_1}{x_2-x_1}\]

Then, the point-slope formula is \[y-y_1 = m(x-x_1)\]or\[y-y_2 = m(x-x_2)\]

Answer 2

is it A @whpalmer4 ??

Answer 3

I was thinking C?

Answer 4

Well, let's see if C works:
\[y+6 = -\frac{1}{2}(x-4)\]for point \((-6,4)\):
\[4+6 = -\frac{1}{2}(-6-4)\]\[10 = -\frac{1}{2}(-10)\]\[10 = 5\]
Uh, nope.

Answer 5

Why were you thinking C? Let's figure out the mistake you made and prevent you from ever doing it again :-)

Answer 6

I don't really know I tried doing it in my head and C just looked right

Answer 7

It was intended to look right, but it isn't :-)

What did you find for the slope?

Answer 8

You mean the 4

Answer 9

The 4?

Answer 10

What did you find for the value of the slope of the line connecting the points (-6,4) and (2,0)?

Answer 11

O wow okay sorry I s lost now, ummm I'll try again

Answer 12

Well, you have a couple of choices. You can actually find the equation of the line going through those points, and select the answer that matches it (this would be my preference, at least from a learning standpoint), or you can try both points in each of the answer choices and select the one that works for both points. In a time-critical situation, the latter might be superior, but it doesn't help you learn how to solve the problem, and you'll be stuck if you ever have to do so without a list of possible answers.

Answer 13

So, my first suggestion was to find the slope of the line through the points \((x_1,y_1) = (-6,4)\) and \((x_2,y_2)=(2,0)\)

Formula for slope (\(m\)) is
\[m = \frac{y_2-y_1}{x_2-x_1} = \frac{0-4}{2-(-6)}=\]Can you tell me what that equals?

Answer 14

Okay well I tried pluging in the numbers to the formulas you gave me on the first response

Answer 15

let's just take it a step at a time. What do you get for \(m\) in that fraction I just wrote?

Answer 16

Okay m=0-4 over 2- negative 6

Answer 17

what does that equal?

Answer 18

-4 over 6

Answer 19

the numerator is correct, but the denominator is not.

2 - (-6) = 2 + 6 = 8

if you think of subtraction of a positive number as moving left on the number line, subtracting a negative number is the same as moving away from the left on the number line, or moving to the right.

Answer 20

Ummm okay so -4 over -6?

Answer 21

No. \[m = \frac{0-4}{2-(-6)} =\frac{-4}{2+6}= \frac{-4}{8} = \]

Answer 22

O okay I see that now but how did you go from 2-(-6) to 2+6?

Answer 23

Subtracting a negative number is the same as adding the absolute value of the negative number...

2- (-6) = 2+|-6| = 2+6 = 8

Answer 24

Okay wait!!! so -4 over 8 is half so that means the only options left is A right!!!!

Answer 25

Again, if you think of subtracting a positive number as moving left on the number line, subtracting a negative number is moving RIGHT on the number line, because negative numbers are the opposite direction from positive numbers

Answer 26

-4/8 is not half, it is negative 1/2...important difference :-)

Answer 27

damnit!!!

Answer 28

Yes, A is the correct answer, but let's check it just the same:

\[y-4 = -\frac{1}{2}(x-(-6))\]\[y-4 =-\frac{1}{2}(x+6)\]
\[4-4 = -\frac{1}{2}(-6+6)\]\[0 = -\frac{1}{2}0\]\[0=0\checkmark\]

\[0-4 = -\frac{1}{2}(2+6)\]\[-4 = -\frac{1}{2}8\]\[-4=-4\checkmark\]

Answer 29

Wow yeah my math was all over the place haha thank you so much I think I kinda somewhat understand it now