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Question

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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Answer 1

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).

2. 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: $$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{-3}{1}=-3$$

3. 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".

Answer 2

now an you just put the answers without explaining them

Answer 3

3