The line of best fit for a scatter plot is shown:
A scatter plot and line of best fit are shown. Data points are located at 1 and 4, 2 and 6, 2 and 3, 4 and 3, 6 and 1, 4 and 5, 7 and 2, 0 and 6. A line of best fit passes through the y-axis at 6 and through the point 4 and 3.
What is the equation of this line of best fit in slope-intercept form? (4 points)
y = −6x + three fourths
y = 6x + three fourths
y = negative three fourthsx + 6
y = three fourthsx + 6
27 answers
y = -3/4x + 6 is the equation of the line of best fit in slope-intercept form.
Which system has infinitely many solutions?
A
−x+y=4
x−y=2
B
3x−y=−7
8x+y=7
C
−2x+2y=−8
x−y=−11
D
−12x+2y=−4
−6x+y=−2
A
−x+y=4
x−y=2
B
3x−y=−7
8x+y=7
C
−2x+2y=−8
x−y=−11
D
−12x+2y=−4
−6x+y=−2
System C has infinitely many solutions.
This can be seen by rearranging the second equation to y=x+11, and then substituting this expression for y into the first equation to get -2x + 2(x+11) = -8. Simplifying gives 0=-6, which is not a true statement. Since the equations are contradictory, this system has infinitely many solutions.
This can be seen by rearranging the second equation to y=x+11, and then substituting this expression for y into the first equation to get -2x + 2(x+11) = -8. Simplifying gives 0=-6, which is not a true statement. Since the equations are contradictory, this system has infinitely many solutions.
Jake scored 28 points in his basketball game by shooting only two-point and three-point shots. He scored a total of 13 baskets.
Write a system of equations to represent the number of each type of basket Jake scored. Explain your thinking.
Solve the system of equations to find the number of each type of basket Jake scored. Show your work.
Write a system of equations to represent the number of each type of basket Jake scored. Explain your thinking.
Solve the system of equations to find the number of each type of basket Jake scored. Show your work.
Let x be the number of two-point shots Jake made and y be the number of three-point shots he made. We can create a system of equations from the given information as follows:
Equation 1: x + y = 13 (Jake made a total of 13 baskets)
Equation 2: 2x + 3y = 28 (Jake scored a total of 28 points)
To see why these equations make sense, note that Equation 1 just expresses the fact that the number of two-point and three-point baskets Jake made adds up to 13. Equation 2 uses the fact that each two-point shot is worth 2 points and each three-point shot is worth 3 points to establish the total number of points Jake scored.
To solve this system of equations, we can use the substitution method. Solving Equation 1 for x in terms of y, we get x = 13 - y. Substituting this expression for x into Equation 2 gives:
2(13 - y) + 3y = 28
Simplifying and solving for y, we get:
26 - 2y + 3y = 28
y = 2
So Jake made 2 three-point shots. Substituting this into Equation 1 to solve for x, we get:
x + 2 = 13
x = 11
Therefore, Jake made 11 two-point shots.
Check: 11(2) + 2(3) = 28, and 11 + 2 = 13, so the solution checks out.
Final answer: Jake made 11 two-point shots and 2 three-point shots.
Equation 1: x + y = 13 (Jake made a total of 13 baskets)
Equation 2: 2x + 3y = 28 (Jake scored a total of 28 points)
To see why these equations make sense, note that Equation 1 just expresses the fact that the number of two-point and three-point baskets Jake made adds up to 13. Equation 2 uses the fact that each two-point shot is worth 2 points and each three-point shot is worth 3 points to establish the total number of points Jake scored.
To solve this system of equations, we can use the substitution method. Solving Equation 1 for x in terms of y, we get x = 13 - y. Substituting this expression for x into Equation 2 gives:
2(13 - y) + 3y = 28
Simplifying and solving for y, we get:
26 - 2y + 3y = 28
y = 2
So Jake made 2 three-point shots. Substituting this into Equation 1 to solve for x, we get:
x + 2 = 13
x = 11
Therefore, Jake made 11 two-point shots.
Check: 11(2) + 2(3) = 28, and 11 + 2 = 13, so the solution checks out.
Final answer: Jake made 11 two-point shots and 2 three-point shots.
The graph of a decreasing linear function intersects the y-axis at (0, 1).
In sets of coordinates that define the function, which of these x-values would have the greatest corresponding y-value?
In sets of coordinates that define the function, which of these x-values would have the greatest corresponding y-value?
Since the function is decreasing, as x increases, y decreases. This means that the y-value corresponding to any x-value less than 0 would be greater than the y-value corresponding to x=0, which we know is 1 based on the y-intercept.
Therefore, there are no x-values that define the function with a greater corresponding y-value than x=0.
Therefore, there are no x-values that define the function with a greater corresponding y-value than x=0.
The Sealey family had a pool installed at their home, and are filling it with water. The number of gallons of water, y, in a pool after x hours is modeled by the graph.
Which statement is TRUE about the y-intercept?
A
The pool is filling at a rate of 55 gallons per hour.
B
The pool is filling at a rate of 110 gallons per hour.
C
The pool originally had 55 gallons in it.
D
The pool was originally empty.
Which statement is TRUE about the y-intercept?
A
The pool is filling at a rate of 55 gallons per hour.
B
The pool is filling at a rate of 110 gallons per hour.
C
The pool originally had 55 gallons in it.
D
The pool was originally empty.
The correct answer is C.
The y-intercept is the point on the graph where x=0. From the graph, we can see that the y-intercept is at (0, 55). This means that when x=0 (i.e., at the beginning), the number of gallons of water in the pool is 55.
Option A is not true because the y-intercept represents the initial amount of water in the pool, not the rate of filling.
Option B is not true because the y-intercept represents the initial amount of water in the pool, not the rate of filling. Additionally, the slope of the line (rate of filling) is not given by the graph.
Option D is not true because the graph clearly shows that there are already 55 gallons of water in the pool at the beginning.
The y-intercept is the point on the graph where x=0. From the graph, we can see that the y-intercept is at (0, 55). This means that when x=0 (i.e., at the beginning), the number of gallons of water in the pool is 55.
Option A is not true because the y-intercept represents the initial amount of water in the pool, not the rate of filling.
Option B is not true because the y-intercept represents the initial amount of water in the pool, not the rate of filling. Additionally, the slope of the line (rate of filling) is not given by the graph.
Option D is not true because the graph clearly shows that there are already 55 gallons of water in the pool at the beginning.
Which terms BEST describe the association of the variables?
A
Nonlinear and positive
B
Linear and negative
C
Nonlinear and negative
D
Linear and positive
A
Nonlinear and positive
B
Linear and negative
C
Nonlinear and negative
D
Linear and positive
Unfortunately, there is no graph, scatter plot, or information given about the variables to provide an answer. Please provide more context for the question.
The scatter plot presents data on the distances of several homes from other locations.
Which terms BEST describe the association of the variables?
A
Nonlinear and positive
B
Linear and negative
C
Nonlinear and negative
D
Linear and positive
Which terms BEST describe the association of the variables?
A
Nonlinear and positive
B
Linear and negative
C
Nonlinear and negative
D
Linear and positive
Unfortunately, there is no accompanying scatter plot to provide an answer. Please provide the scatter plot.
Consider the function y=x+28.3
.
Based on the equation, is the function linear? Explain.
Determine the points on the graph of the function when x
is 0, 1, 2, 3, and 4. Show your work.
Do these points support your answer to Part A? Explain.
Jeanne claims that an equation of the form y=xn+28.3
, where n
is a whole number, represents a nonlinear function. Describe all values of n
for which Jeanne's claim is true and all values of n
for which Jeanne's claim is false. Explain.
.
Based on the equation, is the function linear? Explain.
Determine the points on the graph of the function when x
is 0, 1, 2, 3, and 4. Show your work.
Do these points support your answer to Part A? Explain.
Jeanne claims that an equation of the form y=xn+28.3
, where n
is a whole number, represents a nonlinear function. Describe all values of n
for which Jeanne's claim is true and all values of n
for which Jeanne's claim is false. Explain.
A) Yes, the function is linear.
A function is considered linear if it has a constant rate of change or slope. In this case, y increases by 1 when x increases by 1, meaning the slope is 1. Since the equation of the function is in the form y = mx + b where m is the slope and b is the y-intercept, and its slope is constant, it is a linear function.
B)
When x = 0, y = 28.3
When x = 1, y = 29.3
When x = 2, y = 30.3
When x = 3, y = 31.3
When x = 4, y = 32.3
C) Yes, these points support the answer in part A. The points on the graph indicate a constant rate of change, with y increasing by 1 each time x increases by 1, which is a defining feature of a linear function.
D) Jeanne's claim is true for all values of n other than 1.
If n = 1, y = x^1 + 28.3 simplifies to y = x + 28.3, which is the function given in the question. We know based on Part A that this function is linear, which means Jeanne's claim is false for n=1.
For any other whole number value of n, the function y = xn + 28.3 is nonlinear. This is because as n increases, the graph of the function becomes increasingly steeper (if n > 1) or shallower (if 0 < n < 1) as x increases, meaning the rate of change is not constant, violating the requirement for a function to be considered linear.
A function is considered linear if it has a constant rate of change or slope. In this case, y increases by 1 when x increases by 1, meaning the slope is 1. Since the equation of the function is in the form y = mx + b where m is the slope and b is the y-intercept, and its slope is constant, it is a linear function.
B)
When x = 0, y = 28.3
When x = 1, y = 29.3
When x = 2, y = 30.3
When x = 3, y = 31.3
When x = 4, y = 32.3
C) Yes, these points support the answer in part A. The points on the graph indicate a constant rate of change, with y increasing by 1 each time x increases by 1, which is a defining feature of a linear function.
D) Jeanne's claim is true for all values of n other than 1.
If n = 1, y = x^1 + 28.3 simplifies to y = x + 28.3, which is the function given in the question. We know based on Part A that this function is linear, which means Jeanne's claim is false for n=1.
For any other whole number value of n, the function y = xn + 28.3 is nonlinear. This is because as n increases, the graph of the function becomes increasingly steeper (if n > 1) or shallower (if 0 < n < 1) as x increases, meaning the rate of change is not constant, violating the requirement for a function to be considered linear.
The equation y=−50x+2000
represents the number of people attending a movie where x represents the number of weeks since the movie release and y represents the number of people in the theater.
In the equation, what does the y-intercept indicate?
represents the number of people attending a movie where x represents the number of weeks since the movie release and y represents the number of people in the theater.
In the equation, what does the y-intercept indicate?
The y-intercept in this equation is (0, 2000).
In the context of the problem, this means that when x=0 (i.e., at the time of the movie release), the number of people in the theater is 2000.
Therefore, the y-intercept indicates the initial attendance of the movie.
In the context of the problem, this means that when x=0 (i.e., at the time of the movie release), the number of people in the theater is 2000.
Therefore, the y-intercept indicates the initial attendance of the movie.
The equation y=−50x+2000
represents the number of people attending a movie where x represents the number of weeks since the movie release and y represents the number of people in the theater.
In the equation, what does the y-intercept indicate?
A
Every week the movie is open, the movie theater loses $50.
B
Two thousand people attend the theater during the week of a movie’s release.
C
During a movie’s release week, the movie theater will make $2,000.
D
Every week 50 less people attend the movie theater.
represents the number of people attending a movie where x represents the number of weeks since the movie release and y represents the number of people in the theater.
In the equation, what does the y-intercept indicate?
A
Every week the movie is open, the movie theater loses $50.
B
Two thousand people attend the theater during the week of a movie’s release.
C
During a movie’s release week, the movie theater will make $2,000.
D
Every week 50 less people attend the movie theater.
The y-intercept in the given equation y=-50x+2000 is (0, 2000).
Therefore, the correct option is:
C) During a movie’s release week, the movie theater will make $2,000.
In the given context, the y-intercept always represents the initial value of y, which is the number of people attending the movie or the revenue earned by the theater during the release week of the movie. In this case, the y-intercept is 2000, which represents the revenue (in dollars) that the theater generates during the release week of the movie.
Therefore, the correct option is:
C) During a movie’s release week, the movie theater will make $2,000.
In the given context, the y-intercept always represents the initial value of y, which is the number of people attending the movie or the revenue earned by the theater during the release week of the movie. In this case, the y-intercept is 2000, which represents the revenue (in dollars) that the theater generates during the release week of the movie.
Aaron is considering two health insurance plans. The Get Well Soon Company charges an annual fee of 100
plus 10
per doctor visit, given y=100+10x
. The Mega Coverage Company charges $35 per doctor, with no annual fee, represented by the equation: y=35x
.
Which insurance company has the LOWER rate and what is the rate?
A
Mega Coverage Company, at a rate of 0
B
Mega Coverage Company, at a rate of 35.
C
Get Well Soon, at a rate of 100.
D
Get Well Soon, at a rate of 10
plus 10
per doctor visit, given y=100+10x
. The Mega Coverage Company charges $35 per doctor, with no annual fee, represented by the equation: y=35x
.
Which insurance company has the LOWER rate and what is the rate?
A
Mega Coverage Company, at a rate of 0
B
Mega Coverage Company, at a rate of 35.
C
Get Well Soon, at a rate of 100.
D
Get Well Soon, at a rate of 10
Which situation would represent a positive correlation when graphed as a scatter plot?
A
The amount of time that water is boiling and the amount of water remaining in the pot.
B
The amount of pictures taken and saved on a smartphone and the amount of storage available on the smartphone.
C
The time a cup of coffee sits on a table and the temperature of the coffee.
D
The age of a child from birth to 10 years old and the height of the child.
A
The amount of time that water is boiling and the amount of water remaining in the pot.
B
The amount of pictures taken and saved on a smartphone and the amount of storage available on the smartphone.
C
The time a cup of coffee sits on a table and the temperature of the coffee.
D
The age of a child from birth to 10 years old and the height of the child.
Use the system of equations to answer the question.
2x+y=8
4x+2y=8
What is the solution for this system of equations?
A
(1, 6)
B
(0, -8)
C
no solution
D
infinitely many solutions
2x+y=8
4x+2y=8
What is the solution for this system of equations?
A
(1, 6)
B
(0, -8)
C
no solution
D
infinitely many solutions
The correct answer is C, no solution.
To see why, we can rewrite the second equation as 2(2x + y) = 8, or 4x + 2y = 8. This means that the two equations are equivalent, and represent the same line in the xy-plane.
Therefore, any solution that satisfies the first equation must also satisfy the second equation. However, since the equations are contradictory (one says y=8-2x, the other says y=4-2x), there is no solution that can satisfy both equations at the same time.
To see why, we can rewrite the second equation as 2(2x + y) = 8, or 4x + 2y = 8. This means that the two equations are equivalent, and represent the same line in the xy-plane.
Therefore, any solution that satisfies the first equation must also satisfy the second equation. However, since the equations are contradictory (one says y=8-2x, the other says y=4-2x), there is no solution that can satisfy both equations at the same time.
When a linear function is graphed on the coordinate plane, the line intersects the x-axis at (1, 0), and the rate of change is 3.
Which two points define the linear function?
A
(2, 3), (3, 9)
B
(2, 3), (3, 10)
C
(2, 3), (3, 6)
D
(2, 3), (3, 12)
Which two points define the linear function?
A
(2, 3), (3, 9)
B
(2, 3), (3, 10)
C
(2, 3), (3, 6)
D
(2, 3), (3, 12)
Since the rate of change is 3, the slope of the line (m) is 3. We also know that the line intersects the x-axis at (1, 0), which means that this point must be on the line. We can use this information to find the y-intercept (b).
Using the point-slope form of the equation of a line, we have:
y - 0 = 3(x - 1)
Simplifying, we get:
y = 3x - 3
Therefore, the y-intercept is -3, and two points on the line are:
x = 2, y = 3(2) - 3 = 3 --> (2, 3)
x = 3, y = 3(3) - 3 = 6 --> (3, 6)
Therefore, the answer is C: (2, 3) and (3, 6) define the linear function.
Using the point-slope form of the equation of a line, we have:
y - 0 = 3(x - 1)
Simplifying, we get:
y = 3x - 3
Therefore, the y-intercept is -3, and two points on the line are:
x = 2, y = 3(2) - 3 = 3 --> (2, 3)
x = 3, y = 3(3) - 3 = 6 --> (3, 6)
Therefore, the answer is C: (2, 3) and (3, 6) define the linear function.
A class is taking a field trip. The Science Center charges a flat fee for the entire class plus an additional amount per student to view a special exhibit. This graph represents y
, the total cost in dollars, for x
students.
Which function models the relationship between x
and y
?
A
y=2x+50
B
y=50x
C
y=50x+2
D
y=50−2x
, the total cost in dollars, for x
students.
Which function models the relationship between x
and y
?
A
y=2x+50
B
y=50x
C
y=50x+2
D
y=50−2x
The graph has an initial flat fee of $50, regardless of how many students attend (y-intercept). The additional cost per student is represented by a line with a slope of $2 per student.
This means that for each additional student, the total cost increases by $2.
Using the slope-intercept form (y=mx+b) of a linear function, we can write the equation that models this relationship as:
y = 2x + 50
Therefore, the correct answer is A: y = 2x + 50.
This means that for each additional student, the total cost increases by $2.
Using the slope-intercept form (y=mx+b) of a linear function, we can write the equation that models this relationship as:
y = 2x + 50
Therefore, the correct answer is A: y = 2x + 50.
1 answer