Question

Use the table to answer the question.

x
y

−2
−1

0 1
2 3
Write an equation that represents this nonproportional linear relationship.

(1 point)
Responses

y=x+2
y equals x plus 2

y=12x+1
y equals Start Fraction 1 over 2 End Fraction x plus 1

y=−2x+1
y equals negative 2 x plus 1

y=x+1

Answer 1

A family is going from Dallas, Texas, to Los Angeles, California. They have traveled 500 miles so far. The next day, their average speed is 70 miles per hour. Write an equation for the distance they traveled, y
, and the hours they have driven, x
. Indicate whether this is a proportional or a nonproportional situation.(1 point)
Responses

y=70x+500
, proportional
y equals 70 x plus 500 , proportional

y=70x
, proportional
y equals 70 x , proportional

y=70x+500
, nonproportional
y equals 70 x plus 500 , nonproportional

y=500x+70
, nonproportional

Answer 2

You are baking a cake. For every three cups of flour, you need to add two eggs. Write an equation for the relationship between the number of eggs, y
, and the amount of flour, x
. Distinguish whether this is a proportional or nonproportional situation.(1 point)
Responses

y=23x
, proportional
y equals Start Fraction 2 over 3 End Fraction x , proportional

y=3x+2
, nonproportional
y equals 3 x plus 2 , nonproportional

y=2x+3
, nonproportional
y equals 2 x plus 3 , nonproportional

y=32x
, proportional

Answer 3

To find the equation of a nonproportional linear relationship, we look for a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. **Identify two points from the table:**
From the table, the points are:
- (-2, -1)
- (0, 1)
- (2, 3)

2. **Calculate the slope (m):**
Using the points (0, 1) and (2, 3):
- The formula for slope \( m \) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1
\]

3. **Find the y-intercept (b):**
Using the point (0, 1), we see that when \( x = 0 \), \( y = 1 \). Thus, the y-intercept \( b = 1 \).

4. **Write the equation:**
Now we can substitute the slope and y-intercept into the equation:
\[
y = mx + b \implies y = 1x + 1 \implies y = x + 1
\]

So, the equation that represents this nonproportional linear relationship is:

**y = x + 1**

So the correct response is:

y = x + 1

Answer 4

To determine the equation for the distance traveled \( y \) based on the hours driven \( x \) and to classify the situation as proportional or nonproportional, we analyze the information provided.

1. **Understanding the components:**
- They have traveled 500 miles so far, which means this is the initial distance.
- The next day, they will travel at an average speed of 70 miles per hour.

2. **Writing the equation:**
The total distance traveled can be expressed as the initial distance plus the additional distance covered at the speed of 70 miles per hour for \( x \) hours. Therefore, the equation is:

\[
y = 70x + 500
\]

3. **Classifying as proportional or nonproportional:**
- This situation is **nonproportional** because there is a constant initial distance of 500 miles. A proportional relationship would not have an initial value other than zero.

Thus, the correct response is:

**y = 70x + 500, nonproportional**.

Answer 5

In this situation, you have a relationship between the number of eggs \( y \) and the cups of flour \( x \). For every 3 cups of flour, you need 2 eggs, which creates a constant ratio.

### Step 1: Determine the equation

The relationship can be expressed as:

\[
\frac{y}{x} = \frac{2}{3}
\]

To find the equation in terms of \( y \) in terms of \( x \), we can multiply both sides by \( x \):

\[
y = \frac{2}{3}x
\]

### Step 2: Determine if it is proportional or nonproportional

This equation \( y = \frac{2}{3}x \) indicates that \( y \) is directly proportional to \( x \). If you increase the amount of flour, the number of eggs needed increases in a constant ratio (2 eggs for every 3 cups of flour), and if there is no flour, there are no eggs needed.

Thus, this is a **proportional relationship**.

### Final Answer

The correct response is:

**y = \(\frac{2}{3}\)x, proportional.**