To determine whether the provided graph of the equation \(3x - y = 10\) is correct, we first convert the equation to 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 solve for \(y\): \[ -y = -3x + 10 \] \[ y = 3x - 10 \]
From this form, we can identify:
- The slope \(m = 3\)
- The y-intercept \(b = -10\), which gives the point \((0, -10)\)
Now, let's evaluate the responses:
- "No, it is not the correct graph because the slope is −3 and the y-intercept is (0, −10)." - Incorrect, the slope is \(3\), not \(-3\).
- "No, it is not the correct graph because the slope is negative 3 and the y-intercept is left parenthesis 0 comma negative 10 right parenthesis." - Incorrect, the slope is \(3\).
- "Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10)." - Correct.
- "Yes, it is the correct graph because the slope is 3 and the y-intercept is left parenthesis 0 comma negative 10 right parenthesis." - Correct.
- "Yes, it is the correct graph because the slope is −3 and the y-intercept is (0, −10)." - Incorrect, the slope is \(3\).
- "Yes, it is the correct graph because the slope is negative 3 and the y-intercept is left parenthesis 0 comma negative 10 right parenthesis." - Incorrect, the slope is \(3\).
- "No, it is not the correct graph because the slope is 3 and the y-intercept is (0, −10)." - Incorrect, the slope and y-intercept stated are correct.
- "No, it is not the correct graph because the slope is 3 and the y-intercept is left parenthesis 0 comma negative 10 right parenthesis." - Incorrect, the slope and y-intercept stated are correct.
The correct responses are 3 and 4: "Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10)." and "Yes, it is the correct graph because the slope is 3 and the y-intercept is left parenthesis 0 comma negative 10 right parenthesis."