Question

Ava wrote the expression 4−23−1
to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses

x y
3 4
-1 -2x y 3 4 -1 -2

x y
4 3
2 1x y 4 3 2 1

x y
1 2
3 4


x y 1 2 3 4

x y
4 3
2 1

Answer 1

To find the slope of a line using Ava's expression \( 4 - 2 \cdot 3 - 1 \), we first need to simplify the expression.

1. Perform the operations in order:
- Multiply \( 2 \cdot 3 = 6 \),
- Then the expression becomes \( 4 - 6 - 1 \).

2. Now calculate:
- \( 4 - 6 = -2 \),
- \( -2 - 1 = -3 \).

Thus, the slope calculated from Ava's expression is \(-3\).

The slope of a line is defined as the change in y over the change in x (often represented as \( m = \frac{\Delta y}{\Delta x} \)). A slope of \(-3\) means that for every \( 1 \) unit increase in \( x \), \( y \) decreases by \( 3 \) units.

Now we can analyze the tables provided to identify which could represent a line with a slope of \(-3\):

1. **Table 1:**
- \( (3, 4) \)
- \( (-1, -2) \)
- Change in y: \(-2 - 4 = -6\)
- Change in x: \(-1 - 3 = -4\)
- Slope: \(\frac{-6}{-4} = \frac{3}{2}\) (not \(-3\))

2. **Table 2:**
- \( (4, 3) \)
- \( (2, 1) \)
- Change in y: \(1 - 3 = -2\)
- Change in x: \(2 - 4 = -2\)
- Slope: \(\frac{-2}{-2} = 1\) (not \(-3\))

3. **Table 3:**
- \( (1, 2) \)
- \( (3, 4) \)
- Change in y: \(4 - 2 = 2\)
- Change in x: \(3 - 1 = 2\)
- Slope: \(\frac{2}{2} = 1\) (not \(-3\))

4. **Table 4:**
- \( (1, 2) \)
- \( (2, 3) \)
- Change in y: \(3 - 2 = 1\)
- Change in x: \(2 - 1 = 1\)
- Slope: \(\frac{1}{1} = 1\) (not \(-3\))

No table appears to represent a line with a slope of \(-3\). Please ensure that the tables contain all the pairs that can be used to derive a slope of \(-3\). Given the choices listed, none of the provided tables represent a line with the correct slope of \(-3\).