Question

Annie has created a graph of 3x+y=10 on the coordinate plane. Did Annie create her graph correctly?

Option 1: No; Annie's y -intercept is correct but her slope is incorrect.

Option 2: No; Annie's slope is correct but her y -intercept is incorrect.

Option 3: Yes; Annie's graph is correct.

Enter "1" for Option 1, "2" for Option 2, or "3" for Option 3.

Answer 1

To determine if Annie's graph of the equation \(3x + y = 10\) is correct, we can convert the equation to slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation:

\[
3x + y = 10
\]

we can solve for \(y\):

\[
y = -3x + 10
\]

From this equation, we can see that the slope \(m\) is \(-3\) and the y-intercept \(b\) is \(10\).

Now let's evaluate the options:

- **Option 1** states that Annie's y-intercept is correct but her slope is incorrect. This is false because both the y-intercept (10) and the slope (-3) are correct.

- **Option 2** states that Annie's slope is correct but her y-intercept is incorrect. This is false as well because both values are actually correct.

- **Option 3** states that Annie's graph is correct. This is true because both the slope and y-intercept calculated from the equation are consistent with the graph she created.

Therefore, the correct answer is:

**3**