Direct variation
Y is proportional to x. Use the x value & y value to find a linear model that relates y and x.
x=5, y=9
X=11, y=1.5
y = m x
9 = m * 5
m = 9/5
so
y = (9/5) x
or
5 y = 9 x
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or easier way
x/y = 11/1.5
11 y = 1.5 x
To find a linear model that relates y and x when Y is proportional to x, we can use the formula for direct variation, which states that Y = kx, where k is the constant of variation.
Using the first set of values (x=5, y=9), we can substitute these into the formula to find the value of k:
9 = 5k
Solving for k, we divide both sides of the equation by 5:
k = 9/5 = 1.8
So, the linear model that relates y and x is Y = 1.8x.
Using the second set of values (x=11, y=1.5), we can plug in x and solve for y using this linear model:
Y = 1.8(11)
Y = 19.8
Therefore, when x = 11, according to the linear model Y = 1.8x, y is approximately 19.8.
To find a linear model that relates y and x when y is proportional to x, we can use the formula:
y = kx
where k is the constant of variation. To find k, we can use the given x and y values.
Let's start with the first set of values: x = 5 and y = 9.
Substituting these values into the formula, we get:
9 = 5k
Now, we solve for k by dividing both sides of the equation by 5:
k = 9/5 = 1.8
So, the constant of variation, k, is 1.8.
Now, we can use this value of k to find the linear model for the second set of values: x = 11 and y = 1.5.
Using the formula y = kx and substituting the values, we get:
1.5 = 1.8 * 11
Simplifying further, we get:
1.5 = 19.8
Since this is not a valid equation, it means that the second set of values does not follow the assumed direct variation relationship. Therefore, there is no linear model that relates y and x for the second set of values.