Question

Find the rate of change, y-intercept, and function rule for the pattern below:

1,7,13,19,...
a) 1, 0, y=x
b) 2, 1, y=x+1
c) 3, 5, y=6x
d) 6, 7, y=6x+1

Answer 1

d) 6, 7, y=6x+1. The rate of change is 6, the y-intercept is 1, and the function rule is y = 6x + 1.

Step-by-step explanation:

To find the rate of change, we can subtract each number in the pattern from the previous number. For example: 7 - 1 = 6, 13 - 7 = 6, 19 - 13 = 6. So, the rate of change is 6.

To find the y-intercept, we can look for the starting value in the pattern. In this case, the starting value is 1. So, the y-intercept is 1.

To find the function rule, we can use the pattern to create an equation. Since the rate of change is 6 and the y-intercept is 1, the function rule is y = 6x + 1.