X is partly constant and partly varies as y.when y=2,x=30,and when y=6,x=50.
A.Find the relationship between x and y.
B.Find x when y =3
"X is partly constant and partly varies as y"
---> x = ky + p
when y=2,x=30 ---> 30 = 2k + p
when y=6,x=50 ---> 50 = 6k + p
subtract: 20 = 4k
k = 5
sub back in the first: 30 = 10+p
p = 20
x = 5y + 20
now you can answer B
notice this is just a variation of y = mx + b
x = c + k y
30 = c + 2k
50 = c + 6k
---------------------subtract
-20 = -4k
k = 5
so 30 = c + 10
c = 20
x = 20 + 5 y or y = x/5 -4
and if y = 3 then
x = 20 + 5*3 = 20+15 = 35
if they really know how to do it their self why did they ask for help
To find the relationship between x and y, we need to determine how x changes with respect to y.
Let's start by finding the difference in x when y changes from 2 to 6.
Change in y = 6 - 2 = 4
Change in x = 50 - 30 = 20
Now, we can calculate the rate of change of x with respect to y:
Rate of change = Change in x / Change in y
Rate of change = 20 / 4
Rate of change = 5
This means that for every unit increase in y, x increases by 5.
Now, let's find the value of x when y = 3.
To find this, we can use the relationship we just determined. Since x increases by 5 for every unit increase in y, we can calculate the change in x when y changes from 2 to 3.
Change in y = 3 - 2 = 1
Change in x = Rate of change * Change in y
Change in x = 5 * 1
Change in x = 5
To find the value of x when y = 3, we need to determine the initial value or y-intercept. We can do this by subtracting the change in x from one of the given data points.
Let's subtract the change in x from the x value when y = 2.
x = 30 - 5
x = 25
Therefore, when y = 3, x = 25 + 5 = 30.
So, when y = 3, x = 30.
Do it yourself
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