Question

The table below represents a linear function. xx yy minus, 4−4 2525 minus, 1−1 77 22 minus, 11−11 55 minus, 29−29 Which relationship represents a function with the same slope as the function represented above? Ay, equals, minus, 4, x, plus, 1 y=−4x+1 B x y C x y Dy, equals, start fraction, 5, divided by, 2, end fraction, x, minus, 3 y= 2 5 ​ x−3 Answer

Answer 1

To find a relationship that represents a function with the same slope as the linear function represented in the table, we first need to determine the slope of the original function using the provided points.

From the points given in the table:
1. (-4, 25)
2. (-1, 7)
3. (2, -11)
4. (-29, -29)

Let's calculate the slope (m) using two of these points. We will use the points (-1, 7) and (-4, 25).

The formula for slope between two points (x1, y1) and (x2, y2) is:
\[ m = \frac{y2 - y1}{x2 - x1} \]

Using (-1, 7) and (-4, 25):
- Let (x1, y1) = (-1, 7)
- Let (x2, y2) = (-4, 25)

Plugging in the values:
\[ m = \frac{25 - 7}{-4 - (-1)} = \frac{18}{-3} = -6 \]

Now we have determined that the slope of the original function is -6.

Now, let's check the given options:
A. \( y = -4x + 1 \) (slope = -4)
B. x y (not a function)
C. x y (not a function)
D. \( y = \frac{5}{2}x - 3 \) (slope = \(\frac{5}{2}\))

None of the given options has the same slope of -6. If there are more details or additional options provided, please share them for further analysis!