Question

Use the table to answer the question.

x
y

−5
0
0 5
2 7
Which linear equation represents this nonproportional linear relationship?

(1 point)
Responses

y=−x+5
y equals negative x plus 5

y=15x+5
y equals Start Fraction 1 over 5 End Fraction x plus 5

y=x+5
y equals x plus 5

y=−5x+5
y equals negative 5 x plus 5
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Answer 1

To find the correct linear equation that represents the relationship in the table, we can first look at the provided points:

1. (−5, 0)
2. (0, 5)
3. (2, 7)

From these points, we can identify the y-intercept and the slope to form the equation of the line in the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Determine the y-intercept (b)
Looking at the point (0, 5), we see that when \(x = 0\), \(y = 5\). This tells us that the y-intercept \(b\) is 5.

### Step 2: Calculate the slope (m)
The formula for slope \(m\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (0, 5) and (2, 7):

\[
m = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1
\]

### Step 3: Write the equation
Now we can substitute \(m = 1\) and \(b = 5\) into the slope-intercept form:

\[
y = 1x + 5 \quad \text{or simply} \quad y = x + 5
\]

### Conclusion
The correct linear equation that represents the nonproportional linear relationship based on the provided table is:

**y = x + 5**

Thus, the answer is:

**y = x + 5**