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 x plus 5

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

y=−5x+5
y equals negative 5 x plus 5

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

To find the linear equation that represents the nonproportional linear relationship from the provided points, we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

We have the following points:

• (-5, 0)
• (0, 5)
• (2, 7)

First, let's determine the slope \( m \) using two of the points, for example (0, 5) and (2, 7):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \]

So, the slope \( m = 1 \).

Next, we can find the y-intercept \( b \) using the point (0, 5):

• When \( x = 0 \), \( y = b = 5 \).

Now we can write the equation using the slope and y-intercept:

\[ y = 1x + 5 \] or simply \[ y = x + 5 \]

Thus, the correct response from the options provided is:

y = x + 5