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
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
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.
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.
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.
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?
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.
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.
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.
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