Look at this table:
x y
2
–
11
3
–
21
4
–
31
5
–
41
6
–
51
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Looking at the given table, we can determine that the value of y increases by 10 each time the value of x increases by 1. This suggests a linear relationship between x and y.
To find the equation of the line, we can use the formula for a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Since the value of y increases by 10 each time the value of x increases by 1, the slope (m) is 10. To determine the y-intercept (b), we can use the given value of y when x = 2. From the table, we see that when x = 2, y is unknown. However, we can calculate the y-intercept using the slope and another point on the line.
Let's use the point (3, 21). We know that this point lies on the line, so we can substitute the values of x = 3 and y = 21 into the equation y = mx + b, and solve for b.
21 = 10(3) + b
21 = 30 + b
b = 21 - 30
b = -9
Therefore, the linear function that models the data is:
y = 10x - 9.