To determine whether the graph correctly represents the equation \(3x - y = 10\), we first need to rewrite it in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting from the equation: \[ 3x - y = 10 \]
We can isolate \(y\): \[ -y = -3x + 10 \] \[ y = 3x - 10 \]
From this equation, we can see that the slope \(m\) is \(3\) and the y-intercept \(b\) is \(-10\), which means the y-intercept point is \((0, -10)\).
Now, let's evaluate the provided options based on this information:
- Yes, it is 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 left parenthesis 0 comma negative 10 right parenthesis .
Both responses 1 and 2 correctly state the slope and y-intercept. Therefore, one of these is the correct choice.
The answers mentioning the slope as \(-3\) or indicating any other incorrect y-intercept are incorrect.
So, the correct response is: Yes, it is the correct graph because the slope is 3 and the y-intercept is (0, −10).
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