Question

Days People
1 26
2 30
3 34
4 38
5 42
6 46


Allie is trying to get her classmates to sign up to volunteer at the school carnival. The number of people that had signed up by each day is indicated in the chart. Which line BEST fits the data in the chart?
Responses
A y = 4x - 30y = 4x - 30
B y = 4x + 30y = 4x + 30
C y = 4x - 22y = 4x - 22
D y = 4x + 22

Answer 1

To find the line that best fits the data provided in the chart, we first need to observe the pattern in the number of people signed up as the days progress.

Looking at the data:

- On Day 1: 26 people
- On Day 2: 30 people
- On Day 3: 34 people
- On Day 4: 38 people
- On Day 5: 42 people
- On Day 6: 46 people

From this data, we can see that the number of people signing up increases by 4 each day. This suggests that the slope of our linear equation is 4.

Now, we need to find the y-intercept. If we want to express this in the form of \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept:

1. The slope \(m = 4\).
2. We will use the first data point (1, 26) to find \(b\).

Using the first point (1, 26):

\(y = mx + b\)

Substituting \(x = 1\) and \(y = 26\):

\(26 = 4(1) + b\)

\(26 = 4 + b\)

Now solve for \(b\):

\(b = 26 - 4 = 22\)

So, the equation that models the relationship is:

\(y = 4x + 22\)

Now, let's look at our response options to see which one matches:

A) \(y = 4x - 30\)
B) \(y = 4x + 30\)
C) \(y = 4x - 22\)
D) \(y = 4x + 22\)

The correct answer is **D)** \(y = 4x + 22\).