Question

Suppose y varies directly with x, and y = 8 when x = -6. What direct variation equation relates x and y? What is the value of y when x = -2?

a. y = -0.75x; 1.50
b. y = -1.33x; 2.67
c. y = 1.33x; -2.67
d. y = 0.13x; -0.25

Answer 1

Think the answer's B.

Answer 2

direct variation implies y = kx, for some value of k

You can find k by putting in your known values of x = -6, y = 8 and solving for the value of k. Then use that value in the equation along with x = -2 to find the corresponding value of y.

Answer 3

@KinzaN that's incorrect. be careful about your signs!

Answer 4

D: you must be my math teacher in disguise, I get that often enough.

Answer 5

Why don't you show me the steps you used to find that second answer, which is unfortunately also incorrect?

Answer 6

What step would I use to get the answer. The easiest way. I never learned this because I'm home schooled. I don't know if you know how that works. You have to learn everything on your own.

Answer 7

I described the procedure to use...

y = kx if you have direct variation. (indirect variation would be y = k/x)

we know that y = 8 when x = -6, so that means our equation can be written as

8 = k(-6)
8 = -6k

solve that for k

once you have a value for k, replace the letter k in the equation y = kx with the value, and then plug in x = -2 and find the value of y. that's the answer.

Answer 8

Here is told that @KinzaN was right. http://www.algebra.com/tutors/students/your-answer.mpl?question=833142

Answer 9

@KinzaN my apologies! I misread the order of the answer. k = -4/3, so when x = -2, y = 8/3. I was looking for 8/3, saw the - sign at the start of the answer for B and rejected it.

However, the procedure I outlined is exactly correct; it's just my answer-reading skills that fell short here :-)

Answer 10

Got another problem? I need to redeem myself :-)

Answer 11

Yes. give me a second.

Answer 12

Write the slope-intercept form of the equation for the line.

a. y = -5/8x +1/2
b. y = 8/5x - 1/2
c. y =5/8x + 1/2
d. 8/5x + 1/2

Answer 13

Okay, we have two well-marked points on the line: what are they?

Answer 14

what are the full coordinates? (x,y)

Answer 15

x is the amount right or left of the origin (where the axes cross). y is the amount up or down from the origin. the point on the upper right is at (4,3) because we go over 4 and up 3 to get there from the origin. where is the lower left point?

Answer 16

the x-value is the distance from the y-axis, the line that goes up and down (and is labeled y at the top)

the y-value is the distance from the x-axis, the line that goes right and left (and is labeled x at the right)

the coordinates are written as (x value, y value)

Answer 17

when you've figured out the coordinates of the point on the left, the next step is to determine the slope of the line.

to do this graphically, count how many units along the y-axis the right hand point is higher (or lower) than the left point. call this the "rise". count how many units along the x-axis the right hand point is to the right of the left point. call this the "run". The slope is the rise / run. For example, if we have a point at (0,0) and one at (2,1), the rise = 1-0 = 1, and the run = 2-0 = 2. The slope of a line through those two points would be 1/2. For each unit you go to the right, you also go up 1/2 unit.

You can do this as a formula. Say your two points are (x1, y1) and (x2, y2). The slope, m, is then

m = (y2 - y1)/(x2 - x1)

(it doesn't matter which point you decide is (x1,y1), btw)

Answer 18

now we know the slope, and we know two points. we want to write the slope-intercept form of the equation for the line that passes through those two points. To do so, pick one of the points. Again, it doesn't matter which point you choose. Put that point into the point-slope formula for a line with slope m going through point (x1, y1):

y-y1 = m(x-x1)

rearrange that into slope-intercept form, which is y = mx + b

y - y1 = m(x-x1)
y - y1 = mx - mx1
y = mx - mx1 + y1

now, mx1 and y1 are constants, and you can add them together, giving you the desired slope-intercept form.

Answer 19

as an example, I'll write the slope-intercept form for that line through (0,0) and (2,1). we know m = 1/2. I'll take (2,1) as (x1, y1).

y-y1 = m (x - x1)
y - 1 = (1/2) * (x - 2)
y - 1 = (1/2) * x - (1/2) * 2
y - 1 = (1/2) * x - 1
y -1 + 1 = (1/2) * x - 1 + 1
y = (1/2)*x + 0
that's our slope-intercept form for my example line. it has a slope of 1/2, and a y-intercept (b) of 0.

Answer 20

which one is x? which one is y? there's a convention, and you need use it if you want to be understood.

Answer 21

hint: (x, y) is the convention.

Answer 22

and the x-value is the amount you move to the right or left to get to the point, so please don't write (-2, -4), because the correct location is (-4, -2) :-)

Answer 23

so our two points are:

(x1, y1) = (4, 3)
and
(x2, y2) = (-4, -2)

what do you get for the value of the slope?

Answer 24

is it C?

Answer 25

Ah, this is the other one! Yes, C is correct.