Find the variation constant and an equation of variation where Y varies directly as X and Y=60 when X=10
k=variation constant
y=equation of variation
y=mx+b or y=kx+b (m is the standard symbol, which came to us 300 years ago from the French Academy, headed by Rene Descartes. It has served us well as the symbol for slope).
y=mx+b
60=m*10+b
No since you state y varies directly as x, this implies b=0
m=6
Yikes, so K=0 and y=6? Help please..
To find the variation constant (k) and the equation of variation (y), we need to use the given information that Y varies directly as X and that Y=60 when X=10.
When two variables vary directly, it means that they can be related through a linear equation of the form y = kx, where k is the variation constant.
Here's how we can find the variation constant and the equation of variation:
Step 1: Substitute the given values into the equation y = kx.
We have Y = 60 and X = 10, so the equation becomes 60 = k * 10.
Step 2: Solve the equation for k.
Divide both sides by 10 to isolate k. The equation now becomes 60/10 = k, which simplifies to 6 = k.
Therefore, the variation constant (k) is 6.
Step 3: Write the equation of variation.
Now that we know the value of k, we can rewrite the equation as y = 6x.
So, the equation of variation, where Y varies directly as X, is y = 6x.
In summary:
- The variation constant (k) is 6.
- The equation of variation is y = 6x.