Suppose that y varies directly with x, and y=10 when x=5. What direct variation equation relates x and y? What is the value of y when x=2?
A. y=2x; 4
B. y= 1/2x; 1
C. y=-2x; -4
D. y= 1/10x; 1/5
To determine the direct variation equation that relates x and y, we can use the given information that "y varies directly with x" and "y = 10 when x = 5".
Step-by-step calculations:
1. Start with the general form of direct variation equation: y = kx, where k is the constant of variation.
2. Substitute the given values into the equation:
y = kx
10 = k * 5
3. Solve for k by dividing both sides of the equation by 5:
10/5 = k
2 = k
4. Substitute the value of k back into the direct variation equation:
y = 2x
Now, to find the value of y when x = 2, substitute x = 2 into the direct variation equation:
y = 2x
y = 2 * 2
y = 4
Therefore, the direct variation equation that relates x and y is y = 2x, and when x = 2, the value of y is 4.
The correct answer is A. y = 2x; 4.
To find the direct variation equation that relates x and y, we need to use the given information that "y varies directly with x" and "y=10 when x=5."
In general, a direct variation equation can be written in the form y = kx, where k is the constant of variation.
Using the given information, we can substitute y=10 and x=5 into the equation y=kx:
10 = k * 5
Now, we can solve for k by dividing both sides of the equation by 5:
10/5 = k
k = 2
So, the direct variation equation that relates x and y is y = 2x.
Next, to find the value of y when x=2, we can substitute x=2 into the equation y = 2x:
y = 2 * 2
y = 4
Therefore, the value of y when x=2 is 4.
The correct answer is A. y = 2x; 4.
y varies directly with x -----> y = kx
plug in the given values of x and y and you can find k
Now you have the equation.
replace x with 22 and find y