Question

Use the table to answer the 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=15x+5

Answer 1

To determine the linear equation that represents the given nonproportional linear relationship, we can analyze the provided points.

The points from the table are:
- (-5, 0)
- (0, 5)
- (2, 7)

Let's use two of the points to calculate the slope (m) of the line. We can take the points (0, 5) and (2, 7).

The formula for the slope (m) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using (0, 5) as (x_1, y_1) and (2, 7) as (x_2, y_2):
\[
m = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1
\]

With the slope (m) of 1, we can use the point-slope form of the equation:

\[
y - y_1 = m(x - x_1)
\]

Using the point (0, 5):
\[
y - 5 = 1(x - 0)
\]
\[
y - 5 = x
\]
\[
y = x + 5
\]

Now, let's check the equation against the remaining points to confirm consistency with the nonproportional relationship:
- For x = -5:
\( y = -5 + 5 = 0 \) (matches the point (-5, 0))
- For x = 2:
\( y = 2 + 5 = 7 \) (matches the point (2, 7))

Thus, the equation \( y = x + 5 \) accurately represents the nonproportional linear relationship.

The correct response is:
**y = x + 5**