Question

Ava wrote the expression 4−12−3
to determine the slope of a line. Which table might represent Ava’s line?(1 point)
Responses

x y
3 1
2 4


x y 3 1 2 4

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

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

x y
4 3
2 1

Answer 1

To determine the slope using the expression \(4 - 12 - 3\), let's simplify it step by step:

1. Start with \(4 - 12 = -8\)
2. Then, \(-8 - 3 = -11\)

So, the slope of the line is \(-11\).

The slope \(m\) of a line given by two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We need to find a pair of points from the options provided that gives a slope of \(-11\).

Let’s evaluate each option:

1. **Option 1:**
\[
(3, 1) \quad (2, 4)
\]
\[
m = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \quad \text{(Not -11)}
\]

2. **Option 2:**
\[
(3, 4) \quad (-1, -2)
\]
\[
m = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \quad \text{(Not -11)}
\]

3. **Option 3:**
\[
(4, 3) \quad (2, 1)
\]
\[
m = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \quad \text{(Not -11)}
\]

4. **Option 4:**

This option is identical to option 3 and will yield the same slope.
\[
(4, 3) \quad (2, 1)
\]
\[
m = \frac{1 - 3}{2 - 4} = 1 \quad \text{(Not -11)}
\]

None of the provided options yield a slope of \(-11\). Therefore, based on the calculations, none of the tables represent Ava’s line with a slope of \(-11\).