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An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 10 right parenthesis and left parenthesis 1 comma 7 right parenthesis.

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.

(1 point)
Option
Remaining Attempts : 3
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3 answers

To determine if Annie's graph of the equation \( 3x + y = 10 \) is correct, we need to find the y-intercept and the slope of this equation, and then compare it to the graph described.

  1. Rearranging the equation \( 3x + y = 10 \) into slope-intercept form \( y = mx + b \): \[ y = -3x + 10 \]

From this equation:

  • The slope \( m \) is \(-3\).
  • The y-intercept \( b \) is \(10\) (the point where the line crosses the y-axis).
  1. The graph described has closed points at \( (0, 10) \) and \( (1, 7) \).
  • The point \( (0, 10) \) is indeed the y-intercept, which confirms that the y-intercept is correct.
  • The point \( (1, 7) \) indicates that when \( x = 1 \), \( y = 7 \).

Now, let's check the slope between the points:

  • The change in \( y \) between \( (0, 10) \) and \( (1, 7) \) is: \[ 7 - 10 = -3 \]
  • The change in \( x \) is: \[ 1 - 0 = 1 \]

The slope \( m \) calculated from these points is: \[ m = \frac{\Delta y}{\Delta x} = \frac{-3}{1} = -3 \]

  1. Since both the y-intercept and the slope calculated from the points on the graph match those of the equation \( 3x + y = 10 \), Annie's graph is correct.

Therefore, the correct option is:

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

So, enter "3".

now an you just put the answers without explaining them

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