Use the image to answer the question.

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)

Answer 1

To determine if Annie's graph of the equation \(3x + y = 10\) is correct, we can analyze the equation.

First, we can rewrite the equation in slope-intercept form (y = mx + b):

\[ y = -3x + 10 \]

From this form, we can see that:

• The y-intercept (b) is 10, which means the line crosses the y-axis at the point (0, 10).
• The slope (m) is -3, which indicates that for every 1 unit increase in x, y decreases by 3 units.

Now, we can check the points mentioned. The line passes through (0, 10), which confirms that the y-intercept is correct.

Next, we can check the point (1, 7):

Substituting \(x = 1\) into the equation: \[ y = -3(1) + 10 = -3 + 10 = 7 \]

The point (1, 7) also satisfies the equation, indicating that the slope is indeed correct as the point lies on the line.

Therefore, Annie has correctly plotted both the y-intercept and the slope of the line.

The correct answer is:

3.