Question 1

Question

A)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 x-coordinates. You can determine the run by finding the difference between the y-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 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 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.
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.

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 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.
Question 2
A)
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

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 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 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.
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.

Misha did all steps correctly.
Misha did all steps correctly.
Question 3
A)Which of the following graphed lines is parallel to y=34x+3
?(1 point)
Responses

A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Image with alt text: A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.

A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Image with alt text: A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.

A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Image with alt text: A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.

A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Image with alt text: A line is plotted on a coordinate plane with the x-axis ranging from negative 8 to 8 in increments of 1 and the y-axis ranging from negative 8 to 8 in increments of 1.
Question 4
A)
Use the image to answer the question.

A coordinate graph shows both the x and y axes ranging from negative 5 to 5 in unit increments. Four lines are plotted.

Find the slopes of the lines to determine which lines are perpendicular.

(1 point)
Responses

Line B
is perpendicular to line C
.
Line upper B is perpendicular to line upper C .

Line A
is perpendicular to line D
.
Line upper A is perpendicular to line upper D .

Line C
is perpendicular to line D
.
Line upper C is perpendicular to line upper D .

Line A
is perpendicular to line C
.
Line upper A is perpendicular to line upper C .
Question 5
A)
Use the image to answer the question.

Lines l and n intersect at point upper A. Line l is increasing from left to right and line n is decreasing from left to right. The bottom angle at the point upper A has a right angle symbol.

Given that lines l
and n
are perpendicular, which of the following is part of the proof that l
and n
have slopes that are opposite reciprocals?

(1 point)
Responses

BCCA=−DEAD
cap b cap c over cap c cap A is equal to negative cap d cap e over cap A cap d

The slope of line l
is BCCA
and the slope of line n
is DEAD
.
The slope of line l is cap b cap c over cap c cap A and the slope of line n is cap d cap e over cap A cap d.

△ABC∼△EDA
correct answer only 10 grader level math equations)

Answer 1

Question 1

The correct explanation of 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.

Question 2

Misha did the following incorrectly: Step 3 is incorrect. The lines do not need to have a point of intersection since they are not parallel.

Question 3

As the images are not available for selection, I cannot determine the correct line parallel to \(y = 34x + 3\) without seeing the plots. Generally, any line parallel to this line will have the same slope of 34.

Question 4

To find which lines are perpendicular, the slopes must be opposite reciprocals. Without the graphical information, I can't give a specific answer. However, in general, if line A has a slope of \(m\), line B will be perpendicular to line A if its slope is \(-1/m\).

Question 5

The statement that is part of the proof that lines \(l\) and \(n\) have slopes that are opposite reciprocals is: The slope of line \(l\) is \(BCCA\) and the slope of line \(n\) is \(DEAD\). The slope of line \(l\) is \(\frac{BC}{CA}\) and the slope of line \(n\) is \(-\frac{DE}{AD}\).