Suppose y varies directly with x, and y=15 when x=-5. Find x when y=18.
If y varies directly with x, we can write the equation as y = kx, where k is the constant of variation.
To find the value of k, we can substitute the given values of y and x into the equation. In this case, when y = 15 and x = -5:
15 = k(-5)
Dividing both sides by -5, we get:
k = -3
Now we can use the value of k to find x when y = 18. Substituting y = 18 and k = -3 into the equation:
18 = -3x
Dividing both sides by -3, we get:
x = -6
Therefore, when y = 18, x = -6.
To solve this problem, we can use the equation for direct variation, which is written as y = kx, where k is the constant of variation.
Step 1: Find the value of k
Using the given information, when y = 15 and x = -5, we can substitute these values into the equation:
15 = k(-5)
Simplifying this equation, we have:
-75 = -5k
Dividing both sides by -5, we get:
k = 15.
Step 2: Use the value of k to find x when y = 18
Now we can substitute the value of k into the equation and solve for x:
18 = 15x
Dividing both sides by 15, we have:
x = 18/15
Simplifying, we get:
x = 6/5 or 1.2.
Therefore, when y = 18, x is equal to 1.2.
To find the value of x when y equals 18, we can use the concept of direct variation. Direct variation means that when two variables are directly proportional, they can be expressed as y = kx, where k is the constant of variation.
In this case, since y varies directly with x, we can write the equation as y = kx.
To find the constant of variation (k), we can substitute the given values of y and x into the equation and solve for k. We are given that when x = -5, y = 15.
Substituting these values into the equation, we have 15 = k * -5.
To find k, divide both sides of the equation by -5:
15 / -5 = k * -5 / -5
-3 = k
Now that we have found the value of k, we can use it to find x when y equals 18.
Substitute the values of k and y into the equation:
18 = -3 * x
To solve for x, divide both sides of the equation by -3:
18 / -3 = x
x = -6
Thus, when y equals 18, x equals -6.