Question

teks a.3.c review: graphing linear functions
which statement is true?
select two correct answers.
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

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