Is this the correct graph of 3x−y=10 ? (1 point) Responses No, it is not 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 negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis . 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 . 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 negative 3 and the y -intercept is left parenthesis 0 comma negative 10 right parenthesis . No, it is not 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 left parenthesis 0 comma negative 10 right parenthesis .

Question

GPT-4o mini · Answer

To determine whether the provided graph of the equation $3 x - y = 10$ is correct, we first convert the equation to slope-intercept form ( $y = m x + b$ ), where $m$ is the slope and $b$ is the y-intercept.

Starting with the equation: $3 x - y = 10$

We can rearrange this to solve for $y$ : $- y = - 3 x + 10$ $y = 3 x - 10$

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."