x, y
11, 58
20, 103
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y = mx + b
y = 4.5x + 5
To find the equation of the linear function, we need to determine the values of m and b in the equation y = mx + b.
First, let's find the slope (m) using the formula:
m = (change in y) / (change in x)
Using the coordinates (11, 58) and (20, 103):
change in y = 103 - 58 = 45
change in x = 20 - 11 = 9
m = 45 / 9 = 5
Now, let's find the y-intercept (b) by substituting the values of x and y into the equation y = mx + b. We can use the first set of coordinates (11, 58):
58 = 5(11) + b
58 = 55 + b
b = 58 - 55
b = 3
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3