Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Which sets of ordered pairs have a slope of 2? Select all that apply.

A. [tex]$(1, -4), (2, 6)$[/tex]

B. [tex]$(3, 4), (5, 8)$[/tex]

C. [tex]$(2, 5), (2, 7)$[/tex]

D. [tex]$(5, 7), (4, 5)$[/tex]

E. [tex]$(-2, 4), (0, 5)$[/tex]

F. [tex]$(-2, 4), (1, -2)$[/tex]


Sagot :

To determine which sets of ordered pairs have a slope of 2, we need to calculate the slope for each pair and see if it matches our target slope of 2. The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

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

Let's go through each pair step-by-step:

1. Pair [tex]\((1, -4)\)[/tex] and [tex]\((2, 6)\)[/tex]:
- [tex]\[ m = \frac{6 - (-4)}{2 - 1} = \frac{6 + 4}{2 - 1} = \frac{10}{1} = 10 \][/tex]
- The slope is 10, so this pair does not have a slope of 2.

2. Pair [tex]\((3, 4)\)[/tex] and [tex]\((5, 8)\)[/tex]:
- [tex]\[ m = \frac{8 - 4}{5 - 3} = \frac{8 - 4}{2} = \frac{4}{2} = 2 \][/tex]
- The slope is 2, so this pair does have a slope of 2.

3. Pair [tex]\((2, 5)\)[/tex] and [tex]\((2, 7)\)[/tex]:
- [tex]\[ m = \frac{7 - 5}{2 - 2} = \frac{2}{0} \][/tex]
- Division by zero occurs, so the slope is undefined and not equal to 2.

4. Pair [tex]\((5, 7)\)[/tex] and [tex]\((4, 5)\)[/tex]:
- [tex]\[ m = \frac{5 - 7}{4 - 5} = \frac{5 - 7}{4 - 5} = \frac{-2}{-1} = 2 \][/tex]
- The slope is 2, so this pair does have a slope of 2.

5. Pair [tex]\((-2, 4)\)[/tex] and [tex]\((0, 5)\)[/tex]:
- [tex]\[ m = \frac{5 - 4}{0 - (-2)} = \frac{5 - 4}{0 + 2} = \frac{1}{2} \][/tex]
- The slope is 0.5, so this pair does not have a slope of 2.

6. Pair [tex]\((-2, 4)\)[/tex] and [tex]\((1, -2)\)[/tex]:
- [tex]\[ m = \frac{-2 - 4}{1 - (-2)} = \frac{-2 - 4}{1 + 2} = \frac{-6}{3} = -2 \][/tex]
- The slope is -2, so this pair does not have a slope of 2.

Thus, the pairs with a slope of 2 are:
- [tex]\((3, 4)\)[/tex] and [tex]\((5, 8)\)[/tex]
- [tex]\((5, 7)\)[/tex] and [tex]\((4, 5)\)[/tex]

So, the ordered pairs that have a slope of 2 are:
[tex]\[ (3, 4), (5, 8) \quad \text{and} \quad (5, 7), (4, 5) \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.