Question

Question 11: Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.

scatter plot titled students' data, with the x-axis labeled study time in hours and the y-axis labeled grade percent. Points are plotted at 1 comma 65, 2 comma 60, 2 comma 70, 2 comma 80, 3 comma 70, 3 comma 90, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 50 and 2 comma 70

Determine the equation of the line of fit.

y = 5x + 50
y = 5x + 70
y = 10x + 50
y = 10x + 70

Question 12: Laila participated in a dance-a-thon charity event to raise money for the Animals are Loved Shelter. The graph shows the relationship between the number of hours Laila danced, x, and the money she raised, y.

coordinate plane with the x-axis labeled number of hours and the y-axis labeled total raised in dollars, with a line that passes through the points 0 comma 20 and 5 comma 40

Determine the slope and explain its meaning in terms of the real-world scenario.

The slope is one fourth, which means that the amount the student raised increases by $0.75 each hour.
The slope is 4, which means that the amount the student raised increases by $4 each hour.
The slope is 12, which means that the student will finish raising money after 12 hours.
The slope is 20, which means that the student started with $20.

Question 13: Which graph shows the solution to the system of linear equations?

y equals negative one fourth times x plus 1
y = −2x − 1

a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma 0 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3
a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma 0 and another line that passes through the points 0 comma negative 3 and 1 comma negative 5
a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5
a coordinate grid with one line that passes through the points 0 comma 1 and 4 comma negative 2 and another line that passes through the points 0 comma negative 2 and 1 comma negative 5

Question 14: Which of the following sets of ordered pairs represents a function?

{(−4, −3), (−2, −1), (−2, 0), (0, −2), (0, 2)}
{(−5, −5), (−5, −4), (−5, −3), (−5, −2), (−3, 0)}
{(−4, −5), (−4, 0), (−3, −4), (0, −3), (3, −2)}
{(−6, −3), (−4, −3), (−3, −3), (−2, −3), (0, 0)}

Answer 1

Step-by-step explanation:

Answer 11:

The equation of the line of fit is y = 5x + 50.

Step-by-step explanation:

From the scatter plot, we can see that the line of fit passes through the points (0, 50) and (2, 70). We can find the slope of the line by using the two points:

slope = (change in y) / (change in x) = (70 - 50) / (2 - 0) = 20/2 = 10

Next, we can use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is any point on the line and m is the slope we just found, to find the equation of the line:

y - 50 = 10(x - 0)

Simplifying this equation, we get:

y = 10x + 50

Therefore, the answer is y = 10x + 50.

Answer 12:

The slope is 4, which means that the amount Laila raised increases by $4 for every hour she danced.

Step-by-step explanation:

From the graph, we can see that the line passes through the points (0, 20) and (5, 40). We can find the slope of the line by using the two points:

slope = (change in y) / (change in x) = (40 - 20) / (5 - 0) = 20 / 5 = 4

In the context of the real-world scenario, this means that for every hour Laila danced, she raised an additional $4 towards the charity.

Therefore, the answer is the slope is 4, which means that the amount Laila raised increases by $4 for every hour she danced.

Answer 13:

The graph that shows the solution to the system of linear equations is a coordinate grid with one line that passes through the points 0,1 and 3,-1 and another line that passes through the points 0,-1 and 2,-5.

Step-by-step explanation:

We can solve the system of linear equations y = -1/4x + 1 and y = -2x - 1 by setting the two expressions for y equal to each other and solving for x:

-1/4x + 1 = -2x - 1

Simplifying this equation, we get:

x = 4

Substituting x = 4 into either equation gives us:

y = -1/4(4) + 1 = 0

Therefore, the solution to the system of linear equations is the point (4, 0).

From the answer choices, we can see that the only graph that passes through the point (4, 0) and satisfies the equations of the given lines is the one with one line that passes through the points 0,1 and 3,-1 and another line that passes through the points 0,-1 and 2,-5.

Therefore, the answer is a coordinate grid with one line that passes through the points 0,1 and 3,-1 and another line that passes through the points 0,-1 and 2,-5.

Answer 14:

The set of ordered pairs that represents a function is {(−4, −3), (−2, −1), (0, −2)}.

Step-by-step explanation:

For a set of ordered pairs to represent a function, each input (first coordinate) must correspond to exactly one output (second coordinate). In the given sets of ordered pairs, only one set satisfies this condition: {(−4, −3), (−2, −1), (0, −2)}.