Krystina is trying to derive the slope of a line with coordinates (6, - 2) and (0, 8) using the formula 7 = %-*

Question

Krystin says the slope is because slope 3-8-2=2=1
Is Krystina's calculation for slope correct? If not, what is an appropriate explanation for why she is incorrect?
(1 point)
(1 point)
She is incorrect because she
• calculated the change in y over change in x
She is correct because she
• calculated the change in x over the change in y
She is incorrect because she
• calculated change in x over change in y
She is correct and she simplified the slope correctly
10'
A)
Marco is trying to determine whether the following two lines are Krystina is trying to derive the slope of a line with coordinates (6, - 2) and (0, 8) using the formula 7 = %-*
Krystin says the slope is because slope 3-8-2=2=1
Is Krystina's calculation for slope correct? If not, what is an appropriate explanation for why she is incorrect?
(1 point)
(1 point)
She is incorrect because she
• calculated the change in y over change in x
She is correct because she
• calculated the change in x over the change in y
She is incorrect because she
• calculated change in x over change in y
She is correct and she simplified the slope correctly
10'
A)
Marco is trying to determine whether the following two lines are Krystina is trying to derive the slope of a line with coordinates (6, - 2) and (0, 8) using the formula 7 = %-*
Krystin says the slope is because slope 3-8-2=2=1
Is Krystina's calculation for slope correct? If not, what is an appropriate explanation for why she is incorrect?
(1 point)
(1 point)
She is incorrect because she
• calculated the change in y over change in x
She is correct because she
• calculated the change in x over the change in y
She is incorrect because she
• calculated change in x over change in y
She is correct and she simplified the slope correctly
10'
A)
Marco is trying to determine whether the following two lines are

Answer 1

To determine if Krystina's calculation for the slope is correct, we should first calculate the slope using the coordinates (6, -2) and (0, 8).

The formula for calculating the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in the coordinates:

• Let \((x_1, y_1) = (6, -2)\)
• Let \((x_2, y_2) = (0, 8)\)

Now we calculate:

\[ m = \frac{8 - (-2)}{0 - 6} = \frac{8 + 2}{0 - 6} = \frac{10}{-6} = -\frac{5}{3} \]

From this calculation, we see that the correct slope is \(-\frac{5}{3}\).

In Krystina's statement, it looks like she incorrectly manipulated the points and did not follow the correct formula for finding the slope. The specific phrase "slope 3-8-2=2=1" appears to contain errors.

So, addressing the options provided:

• She is incorrect because she calculated the change in y over change in x: This option aligns with her misunderstanding since she did not calculate it correctly.

• She is correct because she calculated the change in x over the change in y: This option is incorrect; she did not do this.

• She is incorrect because she calculated change in x over change in y: This option would be wrong, as she incorrectly calculated what should be change in y over change in x.

• She is correct and she simplified the slope correctly: This option is incorrect as well since she did not arrive at the correct slope.

The most appropriate statement regarding Krystina's mistake is:

She is incorrect because she calculated the change in y over change in x (but note that her calculation was wrong; just indicating she does not have the method correct is key).

Thus, the best option to mark here is:

She is incorrect because she calculated the change in y over change in x.

Answer 2

Marco is trying to determine whether the following two lines are parallel.
y = }I - 5
Which statement correctly describes the approach Marco should take based on the best reasoning?
Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts.
Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes.
(1 point)
Which Statement describe the approach
Marco should take based on the reasoning?
(1 point)
• Statement #2
• Statement #1

Answer 3

To determine whether two lines are parallel, the key concept is that parallel lines have the same slope but different y-intercepts.

Given this understanding:

• Statement #1: "Marco says he should verify that the lines have the same slope but different y-intercepts." This is the correct reasoning for checking if two lines are parallel.

• Statement #2: "Marco says he should verify that the lines have the same y-intercept but different slopes." This is incorrect, as having the same y-intercept with different slopes means the lines would intersect at one point, thus they are not parallel.

Based on this reasoning, the statement that correctly describes the approach Marco should take is:

• Statement #1