Question

For the table to the​ right, represent the relationship using​ words, an​ equation, and a graph. Then determine whether the relationship is a linear function.
x
y
0
3
1
8
2
13
3
18

Question content area bottom
Part 1
Represent the relationship using words. Choose the correct answer below.
A.
The value of y is ten less than the quantity nine times the value of x.
B.
The value of y is the square of the quantity one plus the value of x.
C.
The value of y is the cube of the quantity seven minus the value of x.
D.
The value of y is three more than the quantity five times the value of x.
Your answer is correct.E.
The value of y is ten less than the square of the quantity ten times the value of x.
F.
The value of y is six times the value of x.
Part 2
Represent the relationship using an equation.
yequals
  
5 x plus 3 ​(Simplify your answer. Type an expression using x as the​ variable.)
Part 3
Graph the relationship. Choose the correct graph below.
A.
0
4
0
20
x
y



x y graph
B.
0
4
0
20
x
y



x y graph
C.
0
4
0
20
x
y

Answer 1

Let's go through each part step by step.

### Part 1: Represent the relationship using words.

To find the correct sentence that describes the relationship between \( x \) and \( y \), we can look at the values provided in the table.

The pairs of \( (x, y) \) are:
- \( (0, 3) \)
- \( (1, 8) \)
- \( (2, 13) \)
- \( (3, 18) \)

We can notice that as \( x \) increases by 1, \( y \) increases by 5. This indicates that there is a consistent linear relationship.

Calculating the values from the equation template given:
- For \( x = 0 \): \( y = 5(0) + 3 = 3 \)
- For \( x = 1 \): \( y = 5(1) + 3 = 8 \)
- For \( x = 2 \): \( y = 5(2) + 3 = 13 \)
- For \( x = 3 \): \( y = 5(3) + 3 = 18 \)

Based on this, the correct answer is:
**D. The value of y is three more than the quantity five times the value of x.**

### Part 2: Represent the relationship using an equation.

Based on the consistent increases in \( y \) as \( x \) changes, the relationship can be written in the form:
\[
y = 5x + 3
\]

### Part 3: Graph the relationship.

Now we need to determine which graph represents the equation \( y = 5x + 3 \).

To help visualize, we can plot the points based on our table:
- For \( x = 0 \), \( y = 3 \), point \( (0, 3) \)
- For \( x = 1 \), \( y = 8 \), point \( (1, 8) \)
- For \( x = 2 \), \( y = 13 \), point \( (2, 13) \)
- For \( x = 3 \), \( y = 18 \), point \( (3, 18) \)

A straight line graph forms from these points since the relationship is linear. You should look for a graph that connects these points and has an upward slope.

Since there's no visual evidence provided, I recommend looking for a graph that accurately shows those points plotted in a straight line and rising steeply.

### Determining if the relationship is a linear function

Since the relationship between \( x \) and \( y \) can be expressed with a linear equation and all changes in \( y \) correspond to consistent and proportional changes in \( x \), **the relationship is indeed a linear function**.

Thus, the summary of your p*arts is:
- Words: **The value of y is three more than the quantity five times the value of x.**
- Equation: \( y = 5x + 3 \)
- The relationship is a **linear function**.