Use the table to answer the question.

Question

x
x
y
y

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

(1 point)
Responses

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

y=x+5
y
=
x
+
5
y equals x plus 5

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

y=1/5x+5

Answer 1

To find the correct linear equation representing the nonproportional linear relationship shown in the table, we can analyze the given points.

The table appears to represent the following points:

• (-5, 0)
• (0, 5)
• (2, 7)

First, we can determine the slope (m) of the line that passes through these points using two of the points, say (0, 5) and (2, 7):

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

Now, we will use the point-slope form of the linear equation y = mx + b to find the y-intercept (b). Since we already found the slope (m = 1), we can substitute one of the points, for example, (0, 5):

\[ y = 1(x) + b \] \[ 5 = 1(0) + b \] \[ b = 5 \]

So, the equation of the line in slope-intercept form is:

\[ y = 1x + 5 \]

This can also be written simply as:

\[ y = x + 5 \]

Now, let’s check if any of the given options match this equation.

The correct option from the provided responses is:

y = x + 5