teks a.3.c review: graphing linear functions\nwhich statement is true?\nselect two correct answers.\na. the…

Explanation:

Step1: Analyze Option A

The y - intercept is the value of y when x = 0. From the graph (assuming the line is related to the grid), if we consider the line (k), we need to check the y - intercept. But wait, maybe there is a typo or mis - reading. Wait, maybe the line is (y=- 2x + 4) (we can infer from other options). The y - intercept of (y = mx + b) is (b). If the line is (y=-2x + 4), the y - intercept is 4. But let's check other options too.

Step2: Analyze Option B

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). If we assume two points on the line of (k), say when (x = 0,y = 4) and (x = 2,y = 0) (from x - intercept). Then (m=\frac{0 - 4}{2-0}=\frac{-4}{2}=-2). So the slope is - 2, so option B is correct.

Step3: Analyze Option C

The zero of a function (k(x)) is the value of (x) when (k(x)=0) (x - intercept). If we solve (y = 0) for (y=-2x + 4), we get (0=-2x + 4), (2x = 4), (x = 2). So the zero (x - intercept) is 2, not 4. So option C is incorrect.

Step4: Analyze Option D

The x - intercept is the value of (x) when (y = 0). For (y=-2x + 4), set (y = 0): (0=-2x + 4), (2x=4), (x = 2). So the x - intercept is 2, so option D is correct. Wait, but the question says "Select two correct answers". Wait, maybe I made a mistake in option A. Wait, the y - intercept: when (x = 0), (y=-2(0)+4 = 4), so y - intercept is 4, so option A is correct? Wait, let's re - check.

Wait, if the line is (y=-2x + 4):

• Y - intercept (x = 0): (y = 4) (option A: "The y - intercept of the graph of k is 4" is correct).
• Slope: (m=-2) (option B: "The slope of the graph of k is - 2" is correct).
• Zero of k: x when y = 0 is 2, so option C: "The zero of k is 4" is incorrect.
• X - intercept: x when y = 0 is 2, so option D: "The x - intercept of the graph of k is 2" is correct. But the question says "Select two correct answers". Wait, maybe the original graph has some other details. Wait, maybe the line is different. Wait, perhaps the user's graph is a vertical or horizontal line? No, the options are about slope and intercepts, so it's a linear function with slope and intercept.

Wait, maybe the correct options are A and B? No, let's re - calculate.

Wait, if the y - intercept is 4 (A is correct), slope is - 2 (B is correct), x - intercept is 2 (D is correct). But the question says "Select two correct answers". Maybe there is a mistake in my assumption. Wait, perhaps the line is (y = - 2x-4)? No, then y - intercept would be - 4.

Wait, the graph in the image has a vertical line? No, the labels are - 1, - 2, - 3, - 4 on the y - axis (downward). Wait, maybe the y - axis is inverted. So the positive y - axis is upward, but the labels are - 1, - 2, - 3, - 4 going down. So the actual y - values: when x = 0, the y - value is 4 (since - 4 is at the bottom, so 4 is at the top). So y - intercept is 4 (A correct). Slope: if we take two points, say (0,4) and (2,0), slope is (\frac{0 - 4}{2-0}=-2) (B correct). X - intercept is 2 (D correct). But the question says "Select two correct answers". Maybe the intended answers are A and B, or B and D, or A and D. Wait, maybe the original problem's line is (y=-2x + 4), so A (y - intercept 4), B (slope - 2), D (x - intercept 2) are correct. But the question says "Select two correct answers". Maybe there is a typo, but based on calculation:

Option B: slope is - 2 (correct).

Option D: x - intercept is 2 (correct).

Or Option A: y - intercept is 4 (correct) and Option B: slope is - 2 (correct).

Wait, let's check the options again:

A. The y - intercept of the graph of k is 4.

B. The slope of the graph of k is - 2.

C. The zero of k is 4.

D. The x - intercept of the graph of k is 2.

If the function is (y=-2x + 4):

• Y - intercept (x = 0): (y = 4) (A correct).

• Slope: (m=-2) (B correct).

• Zero (x when y = 0): (x = 2) (so C incorrect, D correct).

So A, B, D are correct. But the question says "Select two correct answers". Maybe the intended answers are B and D, or A and B, or A and D. But based on the calculations, B and D are correct? Wait, no, A is also correct. Wait, maybe the graph is different. Alternatively, maybe the line is (y = 2x+4), but then slope would be 2. No, the options have slope - 2.

Wait, perhaps the correct options are B and D. Let's confirm:

Slope: - 2 (B correct).

X - intercept: 2 (D correct).

Yes, these two are correct. Or A and B. But let's see:

If y - intercept is 4 (A), slope is - 2 (B), then the equation is (y=-2x + 4), x - intercept is 2 (D). So A, B, D are correct. But the question says "Select two correct answers". Maybe there is a mistake in the problem, but assuming that we have to choose two, let's say B and D.

Answer:

B. The slope of the graph of k is -2, D. The x - intercept of the graph of k is 2