Question

question image
x | y
-1 | 1
2 | -14
5 | -29
8 | -44
q. select all representations below that have the same slope as the table.

Explanation:

To determine the slope of the line represented by the table, we use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step 1: Calculate the slope between the first two points \((-1, 1)\) and \((2, -14)\)

Let \((x_1, y_1) = (-1, 1)\) and \((x_2, y_2) = (2, -14)\).

$$ m = \frac{-14 - 1}{2 - (-1)} = \frac{-15}{3} = -5 $$

Step 2: Verify the slope between the next two points \((2, -14)\) and \((5, -29)\)

Let \((x_1, y_1) = (2, -14)\) and \((x_2, y_2) = (5, -29)\).

$$ m = \frac{-29 - (-14)}{5 - 2} = \frac{-15}{3} = -5 $$

Step 3: Verify the slope between the last two points \((5, -29)\) and \((8, -44)\)

Let \((x_1, y_1) = (5, -29)\) and \((x_2, y_2) = (8, -44)\).

$$ m = \frac{-44 - (-29)}{8 - 5} = \frac{-15}{3} = -5 $$

The slope of the line represented by the table is \(-5\). Any representation (e.g., a line, an equation, another table) with a slope of \(-5\) will have the same slope as the table.

Answer:

The slope of the table is \(\boxed{-5}\). To determine which representations have the same slope, we check if their slope is also \(-5\).