a)It appears that for each increase of 1 in the input, the output increases by 4.
b)The rule in the form of y = mx + b would be:
y = 4x + 7
c)The output would be 35.
b)The input that corresponds to an output of 31 is 6.
Let's analyze the pattern in the given input/output table and answer the questions step by step.
a) Describe in words the pattern relationship.
To describe the pattern, we look at how the output changes as the input increases. Let's calculate the differences between consecutive outputs:
- From input -1 to 0, the output increases by 7 - 3 = 4.
- From input 0 to 2, the output increases by 15 - 7 = 8, and since the input increased by 2, the increase per unit input is 8 / 2 = 4.
- From input 2 to 5, the output increases by 27 - 15 = 12, and since the input increased by 3, the increase per unit input is 12 / 3 = 4.
It appears that for each increase of 1 in the input, the output increases by 4.
b) Write a rule to describe the pattern shown.
To find the rule, we can use the fact that the output increases by 4 times the input. Since the output is 7 when the input is 0, the base value is 7. The rule in the form of y = mx + b would be:
y = 4x + 7
c) If the table had an input of 7, what would be the output?
Substitute x = 7 into the rule:
y = 4(7) + 7
y = 28 + 7
y = 35
d) If the table had an output of 31, what would be the input?
We set y = 31 in the rule and solve for x:
31 = 4x + 7
31 - 7 = 4x
24 = 4x
x = 24 / 4
x = 6