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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

3 answers

To determine which table might represent Ava's line based on the expression she wrote (4 - 12 - 3), let's first simplify that expression:

4 - 12 - 3 = 4 - 15 = -11

This value (-11) does not represent a slope; instead, due to the nature of the choices with two points, we need to identify the slope between the given points.

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

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

Now we can calculate the slopes for each of the provided tables:

  1. Table 1:

    • Points (4, 3) and (2, 1)
    • Slope = \( \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \)

  2. Table 2:

    • Points (3, 1) and (2, 4)
    • Slope = \( \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \)

  3. Table 3:

    • (Same as Table 1: 4, 3) and (2, 1)
    • Slope = \( \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \)

  4. Table 4:

    • Points (3, 4) and (-1, -2)
    • Slope = \( \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \)

Now, summarizing the slopes:

  • Table 1: Slope = 1
  • Table 2: Slope = -3
  • Table 3: Slope = 1
  • Table 4: Slope = \( \frac{3}{2} \)

Given that Ava's slope calculation led to an expression that simplifies to -11 (and we don't directly use it) but the possible slopes derived from combinations of points did not yield meaningful indicators toward her expression, if you're looking for a specific slope representation or a non-ambiguous slope from combinations:

  • If you want to align values aiming to get a specific result, note that neither represented slope aligns with -11 and thus are intrinsic to potentially alternate functions.

Therefore, Tables represented with a slope appear correctly defined, but the differences seem evident towards their relationships without detailed pre-expressions thus ideally:

If you're seeking the values utilizable across those, utilize Table 2 where resulting combination yields oriented negative slope which contrasts distinctly differing from first 2 examples producing positive yielding.

If any points needed are recalibrated for specific needs or suited asks again per table values inputs or derived outputs, let me know!

whats the answer

To determine which table represents a line with a slope that Ava might have calculated, we will calculate the slope for each of the tables presented.

Given the tables:

  1. Table 1:

    • Points: (4, 3) and (2, 1)
    • Slope = \( \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \)

  2. Table 2:

    • Points: (3, 1) and (2, 4)
    • Slope = \( \frac{4 - 1}{2 - 3} = \frac{3}{-1} = -3 \)

  3. Table 3: (same as Table 1)

    • Points: (4, 3) and (2, 1)
    • Slope = \( \frac{1 - 3}{2 - 4} = \frac{-2}{-2} = 1 \)

  4. Table 4:

    • Points: (3, 4) and (-1, -2)
    • Slope = \( \frac{-2 - 4}{-1 - 3} = \frac{-6}{-4} = \frac{3}{2} \)

Now, looking at the slopes calculated from each table:

  • Table 1: Slope = 1
  • Table 2: Slope = -3
  • Table 3: Slope = 1 (same as Table 1)
  • Table 4: Slope = \( \frac{3}{2} \)

Since none of these slopes directly relate to the earlier interpretation of Ava's simplified expression (which yielded -11 and not impactful in linear comparison), we can choose:

Table 2:

  • Slope = -3

This table is the one that includes a negative slope, which might better fit variations of linear reductions determining contrastive descent behaviors.

Final Answer: Table 2 might represent Ava’s line.