Use the table to answer the question.

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
Skip to navigation

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