If y varies diretly with x, write an equation for the direct variation. then find each value.
Find y when x = 10 if y = 8 when x = 20
If think I can find the value by
y/10 = 8/20 with the answer for the value is 4. My problem is how to find the equation. Please explain.
what does "y varies diretly with x" nean?
It means that there is some constant k, such that y = kx.
so, knowing that 8 = k*20 (because they told us that y = 8 when x is 20), we see that k = 8/20, or 2/5.
Thus, y = 2/5 x
when x=10, y = 2/5 * 10 = 4
So, you got the right value for y, but you needed to review just what "y varies diretly with x" means.
To write the equation for direct variation, we need to identify the relationship between the variables involved. In direct variation, when one variable (x) increases or decreases, the other variable (y) also increases or decreases proportionally.
In this case, since y varies directly with x, we can write the equation as follows:
y = kx
The letter 'k' represents the constant of variation. To find the value of 'k,' we can use the given information.
When x = 20, y = 8. We can substitute these values into the equation to solve for 'k':
8 = k(20)
Dividing both sides of the equation by 20 gives us:
8/20 = k
k = 0.4
So, the equation for this direct variation is:
y = 0.4x
To find the value of y when x = 10, we can substitute x = 10 into the equation:
y = 0.4 * 10
y = 4
Therefore, when x = 10, y = 4.