Question

Consider the graph of the linear function below.

Which statements are true? Select ALL that apply.

(Select all that apply.)

A. The point (−4, 0) is on the line.

B. The point (0, −2) is on the line.

C. The point (1, −6) is on the line.

D. The graph represents the equation 2𝑥 − 𝑦 = 4.

E. The graph represents the equation 2𝑥 + 𝑦 = −4.

Answer 1

To determine which statements are true, we need to compare the given points to the equation of the linear function.

The equation of a linear function can be written in the form 𝑦 = 𝑚𝑥 + 𝑏, where 𝑚 is the slope and 𝑏 is the y-intercept.

Looking at the graph, we can see that the line passes through the point (−4, 0), which means the y-intercept is 0. This eliminates options D and E.

To find the slope of the line, we can choose two points on the line and use the formula:

slope (𝑚) = (change in y)/(change in x) = (𝑦2 − 𝑦1)/(𝑥2 − 𝑥1).

Let's choose the points (0, -2) and (1, -6). Plugging in the values, we get:

slope (𝑚) = (-6 - (-2))/(1 - 0) = -4/1 = -4.

Now, we can determine the equation of the linear function since we know the slope and y-intercept.

𝑦 = 𝑚𝑥 + 𝑏

𝑦 = -4𝑥 + 0

This simplifies to

𝑦 = -4𝑥.

Now, we can check if the given points are on the line:

A. The point (−4, 0) is on the line.
Plugging in x = -4 into the equation, we get: 𝑦 = -4(-4) = 16. So, the point (−4, 0) is not on the line. Therefore, statement A is false.

B. The point (0, −2) is on the line.
Plugging in x = 0 into the equation, we get: 𝑦 = -4(0) = 0. So, the point (0, −2) is not on the line. Therefore, statement B is false.

C. The point (1, −6) is on the line.
Plugging in x = 1 into the equation, we get: 𝑦 = -4(1) = -4. So, the point (1, −6) is not on the line. Therefore, statement C is false.

Thus, the correct statements are:

A. The point (−4, 0) is on the line. (False)
B. The point (0, −2) is on the line. (False)
C. The point (1, −6) is on the line. (False)
D. The graph represents the equation 2𝑥 − 𝑦 = 4. (False)
E. The graph represents the equation 2𝑥 + 𝑦 = −4. (False)