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(0, 10), (1, 7)
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.
Option __

1 answer

To determine if Annie created the graph of the equation \(3x + y = 10\) correctly, we can analyze the equation.

First, let's rewrite the equation in slope-intercept form (y = mx + b): \[ y = -3x + 10 \] From this, we can identify:

  • The y-intercept \(b\) is 10.
  • The slope \(m\) is -3.

Now, let's check the points that Annie has indicated on her graph: (0, 10) and (1, 7).

  1. The point (0, 10) corresponds to the y-intercept, which is correct.
  2. For the slope, we calculate the change in y over the change in x between (0, 10) and (1, 7):

\[ \text{Change in } y = 7 - 10 = -3 \] \[ \text{Change in } x = 1 - 0 = 1 \] \[ \text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{-3}{1} = -3 \]

Both the slope and y-intercept match the equation \(3x + y = 10\).

Since Annie's y-intercept is correct and her slope is also correct, the correct option is:

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

Enter "3".