Question

Ava wrote the expression 4−12−3 to determine the slope of a line. Which table might represent Ava’s line?(1 point)Responsesxy34-1-2x y 3 4 -1 -2xy4321x y 4 3 2 1xy4321x y 4 3 2 1xy3124

Answer 1

To determine the slope of a line from the expression \(4 - 12 - 3\), we first simplify it:

\[
4 - 12 - 3 = 4 - 15 = -11
\]

However, it seems Ava intended to calculate the slope, which is typically represented as \(\frac{\text{change in } y}{\text{change in } x}\).

In order to find a table representing a line with a slope of \(-11\), we need to look for pairs of points in the tables that demonstrate this slope.

The slope of -11 means that for every unit increase in \(x\), \(y\) decreases by 11 units.

Let's evaluate the tables given in the responses:

1. **First Table:**
- For points (3, 4), (2, -1):
- Change in \(y\) = -1 - 4 = -5
- Change in \(x\) = 2 - 3 = -1
- Slope = \(\frac{-5}{-1} = 5\) (not -11)

2. **Second Table:**
- For points (4, 3), (3, 2):
- Change in \(y\) = 2 - 3 = -1
- Change in \(x\) = 3 - 4 = -1
- Slope = \(\frac{-1}{-1} = 1\) (not -11)

3. **Third Table:**
- For points (4, 3), (3, 2), (2, 1), and (1, 0):
- Same as above, slope is 1 (not -11)

4. **Fourth Table:**
- For points (3, 1), (2, 4):
- Change in \(y\) = 4 - 1 = 3
- Change in \(x\) = 2 - 3 = -1
- Slope = \(\frac{3}{-1} = -3\)

None of these tables appear to represent a slope of -11.

If we want to construct a line with a slope of -11, consider the points:
- If the first point is (0, 0), the second point would be (1, -11).

So, we could have a table like:
- (0, 0)
- (1, -11)

To find an exact match from your options:
None of the provided tables seem to fit the slope of -11. All given tables represent different slopes.

Please check the tables again or provide additional context.