Use the table to answer the question.
X
4
6
Y
38
58
Write the equation of the linear function that models the relationship shown in the table.
To find the equation of the linear function, we need to determine the slope and y-intercept.
First, find the slope (m) by using the formula:
m = (change in Y)/(change in X)
In this case, the change in Y is 58 - 38 = 20, and the change in X is 6 - 4 = 2.
So, the slope is m = 20/2 = 10.
Next, find the y-intercept (b) by substituting one of the given points into the slope-intercept form of the equation: y = mx + b.
Using the point (4, 38), we have:
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2.
Therefore, the equation of the linear function that models the relationship shown in the table is y = 10x - 2.