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
4 3
2 1
x y 4 3 2 1

x y
3 1
2 4


x y 3 1 2 4

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

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

Answer 1

To determine which table might represent Ava's line using the expression \(4 - 12 - 3\), we first need to evaluate the expression.

Simplifying it:

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

However, this expression might be incorrectly interpreted or miscommunicated. Instead, if we assume Ava is trying to find the slope of a line defined by two points (for example, using the points at (4, 3) and (2, 1)), we can calculate the slope using the formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1}. \]

Let's calculate the slope for the first table:

**For the first table:**

Points: (4, 3) and (2, 1)

\[
\text{slope} = \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1.
\]

**For the second table:**

Points: (3, 1) and (2, 4)

\[
\text{slope} = \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3.
\]

**For the third table:**

Same as the first table, so it will also yield a slope of 1.

**For the fourth table:**

Points: (3, 4) and (-1, -2)

\[
\text{slope} = \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2}.
\]

Summarizing:

- The first and third tables yield a slope of 1.
- The second table yields a slope of -3.
- The fourth table yields a slope of \( \frac{3}{2} \).

Ava likely determined the slope using the standard slope formula, which means the table with points yielding the slope of 1 (either the first or third table) would align best with her expression.

Therefore, the correct response is:

**The first table:**

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