Suppose y varies directly with x, and y = 14 when x = –4. What is the value of y when x = –6?
(1 point)
Responses
–21
–21
10
10
18
18
21Suppose y varies directly with x, and y = 14 when x = –4. What is the value of y when x = –6?
(1 point)
Responses
–21
–21
10
10
18
18
21
To find the value of y when x = -6, we use the direct variation equation: y = kx.
From the information given, we know that y = 14 when x = -4. Plugging these values into the direct variation equation, we can find the value of k:
14 = k(-4)
Dividing both sides by -4: k = -14/-4 = 3.5
Now, we can use the value of k to find y when x = -6:
y = 3.5(-6) = -21
Therefore, the value of y when x = -6 is -21.
To solve this problem, we can use the direct variation equation y = kx, where k represents the constant of variation.
Given that y = 14 when x = -4, we can substitute these values into the equation to solve for k.
14 = k(-4)
Next, we'll solve for k by dividing both sides of the equation by -4:
k = 14 / -4
k = -3.5
Now that we have the value of k, we can use it to find the value of y when x = -6. Substitute -6 for x in the direct variation equation:
y = (-3.5)(-6)
Simplifying the equation, we have:
y = 21
The value of y when x = -6 is 21.
are you sure
To solve this problem, you can use the concept of direct variation. Direct variation means that there is a constant ratio between the two variables involved. In this case, y varies directly with x means that the ratio of y to x is constant.
To find that constant ratio, you can use the given information. We are given that when x is -4, y is 14. This means that the ratio of y to x is 14 divided by -4.
Now, we can use this ratio to find the value of y when x is -6. Since the ratio is constant, we can set up the equation:
14 / -4 = y / -6
To solve this equation, we can cross multiply:
14 * -6 = -4 * y
-84 = -4 * y
To find the value of y, divide both sides of the equation by -4:
y = -84 / -4
Simplifying the expression:
y = 21
Therefore, the value of y when x is -6 is 21.