Question

Briella is trying to remember the formula for slope. Which of the following explanations of slope could help her figure out the formula?(1 point)
Responses

Slope is the ratio of rise over run. When given two points, you can determine the rise by finding the difference between the y-coordinates. You can determine the run by finding the difference between the x-coordinates.

Slope is the ratio of run over rise. When given two points, you can determine the rise by finding the difference between the y -coordinates. You can determine the run by finding the difference between the x -coordinates.

Slope is the ratio of rise over run. When given two points, you can determine the rise by finding the difference between the x -coordinates. You can determine the run by finding the difference between the y -coordinates.

Slope is the ratio of run over rise. When given two points, you can determine the rise by finding the difference between the x-coordinates. You can determine the run by finding the difference between the y-coordinates.

Answer 1

Misha writes the following proof that two distinct lines, l
and n
, with the same slope, m
, are parallel. She uses a proof by contradiction. Which step did she do incorrectly?

Assume that distinct lines l
and n
have the same slope, m
, but are not parallel.
Let l
have the equation y=mx+b
and n
have the equation y=mx+c
. In order to be distinct lines, it must be true that b≠c
.
Since they are assumed to not be parallel, they must have a point of intersection.
Set the equations for l
and n
equal to each other and solve to find the x
-coordinate of the point of intersection.
Setting mx+b
equal to mx+c
results in b=c
, which contradicts the condition that b≠c
.
Therefore the assumption that two distinct lines with the same slope are not parallel is incorrect. It must be true that two distinct lines with the same slope are parallel.
(1 point)
Responses

Misha did all steps correctly.
Misha did all steps correctly.

Step 2 is incorrect. In order to be distinct lines, it must be true that b=c
.
Step 2 is incorrect. In order to be distinct lines, it must be true that b is equal to c.

Step 3 is incorrect. The lines do not need to have a point of intersection since they are not parallel.
Step 3 is incorrect. The lines do not need to have a point of intersection since they are not parallel.

Step 5 is incorrect. Both equations need to be solved for x
first, then set equal to each other in order to directly solve for the x
-intercept.

Answer 2

Calculate the slope of the line based on the two points in the graph. Leave the answer in simplest fraction form, if it applies. If the slope is undefined, enter a value of 100.

line: (-4,5) (8,-1)

Answer 3

The explanation that could help Briella figure out the formula for slope is:
"Slope is the ratio of rise over run. When given two points, you can determine the rise by finding the difference between the y-coordinates. You can determine the run by finding the difference between the x-coordinates."

Answer 4

The incorrect step is:
"Step 2 is incorrect. In order to be distinct lines, it must be true that b=c."

Answer 5

To calculate the slope of the line based on the two points (-4,5) and (8,-1), we can use the formula:

slope = (change in y-coordinates) / (change in x-coordinates)

The change in y-coordinates is -1 - 5 = -6, and the change in x-coordinates is 8 - (-4) = 12.

Therefore, the slope of the line is -6/12, which simplifies to -1/2.

So, the slope of the line is -1/2.