Question

Is this the correct graph of ?
(1 point)
3x − y = 10
Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, − 10).
No, it is not the correct graph because the slope is −3 and the y-intercept is (0, − 10).
Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, − 10).
No, it is not the correct graph because the slope is 3 and the y-intercept is (0, − 10).

Answer 1

To determine if the statements regarding the graph of the equation \(3x - y = 10\) are correct, we should first convert the equation into slope-intercept form (\(y = mx + b\)), where \(m\) is the slope and \(b\) is the y-intercept.

1. Start with the equation:
\[
3x - y = 10
\]

2. Solve for \(y\):
\[
-y = -3x + 10
\]
\[
y = 3x - 10
\]

From this form, we can see that:
- The slope \(m\) is **3**.
- The y-intercept \(b\) is **-10**, which is the point \((0, -10)\).

Now let's evaluate the options provided:

- **Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, − 10).** (Incorrect: Slope is 3, not -3.)
- **No, it is not the correct graph because the slope is −3 and the y-intercept is (0, − 10).** (Incorrect: Slope is 3, not -3.)
- **Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, − 10).** (Correct: Slope is 3 and y-intercept is -10.)
- **No, it is not the correct graph because the slope is 3 and the y-intercept is (0, − 10).** (Incorrect: This statement contradicts the correct information.)

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