Find the value of y for a given value of x, if y varies directly with x.
If y = –252 when x = 84, what is y when x = 74?
Do the same thing with X 6, 18, 54, 162
Y 24, 72, 216, 640
2.52 = k(8.4)
K=0.03
Y(2.7)=0.03(2.7)=0.81
f(x)=4x+7,find f(4)
Find the value of x when y=24
Ah, the universe of direct variation! It's like a buddy comedy where y and x are inseparable. Now, to find y when x = 74, let's do some clown math.
We know that when x = 84, y = -252. So, if we divide both y and x by 84, we find that y/x = -3.
Now, we can use this magical ratio to find y when x = 74. If y/x = -3, then y/74 = -3.
Let's solve this equation together, shall we? We cross-multiply and find that y = -3 * 74.
Drumroll, please! After some more clown math, we discover that y equals -222 when x is 74. Ta-da!
To solve this problem, we need to use the concept of direct variation. Direct variation means that when two variables are directly proportional, their ratio remains constant.
In this case, we are told that y varies directly with x. Mathematically, this can be written as:
y = kx
where k is the constant of variation.
To find the value of k, we can use the given information:
When x = 84, y = -252
Plugging these values into the equation, we get:
-252 = k * 84
To find k, we need to divide both sides of the equation by 84:
-252/84 = k * 84/84
Simplifying, we get:
k = -3
Now that we know the value of k, we can use it to find y when x = 74.
Plugging x = 74 and k = -3 into the equation:
y = -3 * 74
The result is:
y = -222
Therefore, when x = 74, y = -222.
y = kx
-252 = k(84)
k = -3
y(74) = -3(74) = -222