Question

Use the image to answer the 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

Answer 1

To determine if Annie created her graph of the equation \(3x + y = 10\) correctly, we'll analyze the slope and y-intercept of the line represented by this equation.

1. **Rearranging to slope-intercept form (y = mx + b)**:
\[
y = -3x + 10
\]
Here, the slope \(m\) is \(-3\), and the y-intercept \(b\) is \(10\).

2. **Identifying points on the line**:
- The y-intercept is at the point \((0, 10)\), which is correct since the line includes this point.
- To find another point, substitute \(x = 1\) into the equation:
\[
y = -3(1) + 10 = -3 + 10 = 7
\]
So, another point on the line is \((1, 7)\), which also matches the points given in the original question.

3. **Analyzing the slope**:
- The slope calculated is \(-3\). The line measured in the illustration is downward slanting, which is consistent with a negative slope.

Since both the points plotted and the slope are checked and found to be correct:

**The correct option is: 3 (Yes; Annie's graph is correct.)**