A table of values is representing a linear relationship is shown.

Question

x
-2
0
2
4
y
-7
-3
1
5
Which equation models this relationship in slope-intercept form?

(1 point)
Responses

y=2x−3
y is equal to 2 x minus 3

y=−2x−3
y is equal to negative 2 x minus 3

y=12x−3
y is equal to 1 half x minus 3

y=−4x−3
y is equal to negative 4 x minus 3

y=3x−3
y is equal to 3 x minus 3

y=2x−7
y is equal to 2 x minus 7

y=2x−5
y is equal to 2 x minus 5

y=−2x−1
y is equal to negative 2 x minus 1

y=12x−7

Answer 1

To find the equation that models the linear relationship presented by the given table of values, we need to calculate the slope (m) and the y-intercept (b) of the line in slope-intercept form, which is expressed as \( y = mx + b \).

From the table:

\[ \begin{array}{c|c} x & y \ \hline -2 & -7 \ 0 & -3 \ 2 & 1 \ 4 & 5 \ \end{array} \]

We can calculate the slope \( m \) using any two points from the table. Let's take the points \( (0, -3) \) and \( (2, 1) \):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{2 - 0} = \frac{4}{2} = 2 \]

Now, using the slope \( m = 2 \) and the point \( (0, -3) \) (where \( x = 0 \) gives us the y-intercept \( b \)), we can express the equation as:

\[ y = 2x + b \]

Since when \( x = 0 \), \( y = -3 \):

\[ -3 = 2(0) + b \implies b = -3 \]

Thus, the equation in slope-intercept form is:

\[ y = 2x - 3 \]

The correct response is:

y = 2x - 3