Suppose y varies directly with x, and y = 15 and x = 5. Write a direct variation equation that relates x and y. What is the value of y when x 9?
" ..y varies directly with x" ---> y = kx
when y=15, x=5
15 = k(5)
k = 3
so y =3k
then when x = 9, y = 27
Oh, direct variation, how direct you are! We can write the direct variation equation as y = kx, where k is the constant of variation.
Now, since y = 15 when x = 5, we can substitute these values into the equation to find k:
15 = k * 5
Dividing both sides by 5, we find:
k = 3
So, the direct variation equation that relates x and y is y = 3x.
Now, if we plug in x = 9, we can calculate the value of y:
y = 3 * 9
y = 27
So, when x = 9, y would be equal to 27. Ta-da!
To write the direct variation equation that relates x and y, we can use the formula:
y = kx
where k is the constant of variation.
Given that y = 15 and x = 5, we can substitute these values into the equation and solve for k:
15 = k * 5
Divide both sides of the equation by 5:
k = 15 / 5
k = 3
Therefore, the direct variation equation that relates x and y is:
y = 3x
To find the value of y when x = 9, we can substitute x = 9 into the equation:
y = 3 * 9
y = 27
So, when x is 9, y is 27.
When a variable y varies directly with another variable x, it can be represented by the equation y = kx, where k is the constant of variation.
In this case, we know that y = 15 when x = 5. To find the constant of variation, we can substitute these values into the equation: 15 = k(5).
Dividing both sides of the equation by 5, we can solve for k: 3 = k.
Now that we have the constant of variation (k = 3), we can write the direct variation equation: y = 3x.
To find the value of y when x = 9, we can substitute x = 9 into the equation: y = 3(9).
Evaluating the expression, we get: y = 27.
Therefore, when x = 9, the value of y is 27.