Question

Use the image to answer the question.
(1, -7), (0, 10)
Is this the correct graph of 3x - y = 10?
A. Yes, it is the correct graph because the slope is -3 and the y-intercept is (0, -10).
B. No, it is not the correct graph because the slope is 3 and the y-intercept is (0, -10).
C. Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).
D. No, it is not the correct graph because the slope is -3 and the y-intercept is (0, -10).

Answer 1

To determine whether the graph corresponds to the equation \(3x - y = 10\), we need to rewrite the equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the equation:

\[ 3x - y = 10 \]

We can rearrange this to isolate \(y\):

\[ -y = -3x + 10 \]

Multiply both sides by -1:

\[ y = 3x - 10 \]

From this, we can see that:

- The slope \(m\) is 3.
- The y-intercept is \((0, -10)\).

Now, to evaluate the answer choices:

- A states the slope is -3, which is incorrect.
- B states the slope is 3 (correct) but the y-intercept is also wrong, as it should be (0, -10).
- C states the slope is 3 and the y-intercept is (0, -10), which is correct.
- D states the slope is -3, which is also incorrect.

The correct answer is:

**C. Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, -10).**