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

Question

x y
-2 -7
0 -3
2 1
4 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=1/2x−7

Answer 1

To find the equation that models the linear relationship given the table of values, we can first determine the slope (\(m\)) and the y-intercept (\(b\)) of the linear equation in slope-intercept form, which is \(y = mx + b\).

Given the points from the table:

• (-2, -7)
• (0, -3)
• (2, 1)
• (4, 5)

1. Calculate the slope (\(m\)):

Using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

We can choose any two points. Let’s use (0, -3) and (2, 1): \[ m = \frac{1 - (-3)}{2 - 0} = \frac{1 + 3}{2} = \frac{4}{2} = 2 \]

2. Determine the y-intercept (\(b\)):

Using the slope and one of the points (we can use (0, -3)): \[ y = mx + b \implies -3 = 2(0) + b \implies b = -3 \]

3. Equation of the line:

Now that we have \(m = 2\) and \(b = -3\), we can write the equation: \[ y = 2x - 3 \]

Thus, the equation that models this relationship in slope-intercept form is:

y = 2x − 3

So the correct response is: y = 2x − 3