Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
To find the equation of the linear function in the form y = mx + b, we need to find the values of m (slope) and b (y-intercept).
Using the given table, we can find the slope (m) by finding the difference in y-values divided by the difference in x-values for any pair of points.
For example, if we choose the points (6, 16) and (15, 43):
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3
Now that we have the slope, we can find the y-intercept (b) by substituting the slope and one set of coordinates from the table into the equation y = mx + b and solving for b.
Using the point (6, 16):
16 = 3(6) + b
16 = 18 + b
b = -2
Therefore, the equation that models the relationship shown in the table is:
y = 3x - 2