if y varies directly as x and y=4 when x= -2, find y when x=30?

Question

a. -4/15
b. 60
c. -60
d. 4/15

Answer 1

c. -60.

These sorts of problems suggest a constant of proportionality exists between x and y. The trick is to find it and use it. Such equations are usually expressed as:

y = kx, where k is the constant of proportionality.

Since you are given y = 4 when x = -2, you can find the constant of proportionality easily. Just substitute these values directly into the equation y = kx and solve for k. Then you can use that value for k to find any x or y when given the other.

4 = k (-2)
4/(-2) = k
-2 = k

Now use k = -2 to find the y value when x = 30.

y = kx ----> y = (-2)(30) ----> y = -60.

Answer 2

use a proportion:

4/-2 =y/30
120/-2 =y

y=-60

Answer 3

So

y = -2x, right? -2 * -2 = 4.
So if x = 30 y should be -60.

(c)

Answer 4

basically refering to the derivative of y with respect to x, ie the gradient.
m= change in y / change in x

y = m x , thus answer is -60

Answer 5

c. -60