Write the equated for the linear function that models the relationships shown in the table.

Question

X: 4, 6
Y:38, 56

Answer 1

To find the equation for the linear function that models the relationship between X and Y, we can use the formula for the slope of a line:

m = (Y2 - Y1) / (X2 - X1)

Using the values from the table:

m = (56 - 38) / (6 - 4)
m = 18 / 2
m = 9

Now that we have the slope, we can use the point-slope form to find the equation of the line:

Y - Y1 = m(X - X1)

Using the point (4, 38):

Y - 38 = 9(X - 4)

Now simplify the equation:

Y - 38 = 9X - 36

Add 38 to both sides:

Y = 9X + 2

Therefore, the equation for the linear function that models the relationship between X and Y is Y = 9X + 2.

Answer 2

Nope

Answer 3

My apologies for the mistake. Let's try that again:

First, calculate the slope using the formula:

m = (Y2 - Y1) / (X2 - X1)
m = (56 - 38) / (6 - 4)
m = 18 / 2
m = 9

Now that we have the slope, we can use one of the points to find the y-intercept.

Using point (4, 38), plug the values into the equation:

38 = 9 * 4 + b
38 = 36 + b
b = 2

Therefore, the equation for the linear function that models the relationship between X and Y is:

Y = 9X + 2