Question

Find the value of y so that the line passing through (9, 0) and (3, y) has a slope of -1/2. If someone could explain this a little bit better.

Answer 1

Formula for the slope given two points \(\large (x_1 \ , \ y_1)\) and \(\large(x_2 \ , \ y_2)\)
\[\Large m = \frac{y_2-y_1}{x_2-x_1}\]

Answer 2

Compactly,
\[\Large m = \frac{\Delta y}{\Delta x}\]

Answer 3

what do those triangles mean

Answer 4

They mean difference. It's just a shorter way of writing \[\Large m = \frac{y_2-y_1}{x_2-x_1}\]

Those 'triangles' are the uppercase Greek letter Delta, which means difference, so in effect,
\[\Large m = \frac{\Delta y}{\Delta x}\]
just means 'difference of y's divided by difference of x's'

If those 'triangles' look that much alien to you, then pay no heed to them, and just focus on this slope formula:
\[\Large m = \frac{y_2-y_1}{x_2-x_1}\]

Answer 5

well what do i do with the given y in the problem

Answer 6

Well, you can consider that y to be your \(y_2\)

Answer 7

(9,0) and (3,y) how do i subtract it like that

Answer 8

the y i mean

Answer 9

What are the y-values of these two points? By y-values, I mean the right-coordinates...

Answer 10

0 and y

Answer 11

And their difference is...?

Answer 12

-1/2? or is it the other coordinates which would be 9 and 3?

Answer 13

No, the difference of 0 and y.
So y - 0 = y
:P

Answer 14

Their difference is y. Got that so far?

Answer 15

so y is 0..?