You buy 3 pounds of organic apples for $7.50. The graph shows the price for regular apples. What is the unit rate for each type of apple?
A line is shown on a coordinate graph. The horizontal axis is titled pounds. The line passes through the origin and the points with coordinates 1 comma 2, 2 comma 4, and 3 comma 6.
A. organic $2.50/pound; regular $3.00/pound
B. organic $0.40/pound; regular $0.50/pound
C. organic $2.50/pound; regular $2.00/pound
D. none of the above
To find the unit rate, we need to divide the price by the number of pounds.
For the organic apples, we know that 3 pounds cost $7.50, so the unit rate is:
$7.50 ÷ 3 pounds = $2.50/pound
For the regular apples, we can use the graph to find the price for 1 pound, which is the same as the slope of the line. From the graph, we can see that for every 1 pound increase in weight, the price increases by $1. This means that the unit rate is:
$1 ÷ 1 pound = $1/pound
Therefore, the unit rate for regular apples is $1/pound, not one of the answer choices given.
The price for pears is y = 2.75x. Which line would have the steepest slope if organic apples and pears were added to the graph?
A. organic apples
B. pears
C. regular apples
D. We need more information to answer this question.
The slope is a measure of how steep a line is. In this case, the slope of the line representing pears is 2.75, which means that for every 1 increase in the x-value (weight), the y-value (price) increases by $2.75.
To compare this to the slope of other lines, we would need to know the prices of organic apples and regular apples, as well as how they relate to weight. Without this information, we cannot determine which line would have the steepest slope if organic apples and pears were added to the graph.
Therefore, the answer is D: We need more information to answer this question.
What is the rule for the function shown in the table?
A table is shown with the first row titled x and the second row titled y.
The first row contains the numbers negative 1, 0, 1, and 2.
The second row contains the numbers negative 2, 1, 4, and 7.
A. y equals one-third x plus 1
B. y = 3x + 1
C. y equals one-third x
D. y equals one-half x plus 1
To determine the rule for the function, we need to look for a pattern or relationship between the inputs (x-values) and outputs (y-values) in the table.
From the table, we can see that when x increases by 1, y increases by 3. This means that there is a constant rate of change of 3 between the x and y values.
To express this relationship in an equation, we can use the slope-intercept form:
y = mx + b
Where m is the slope (rate of change) and b is the y-intercept.
Since the slope is 3, we know that the equation must start with y = 3x + b.
To find b, we can substitute one of the ordered pairs from the table. For example, when x = 0, y = 1. Substituting these values, we get:
1 = 3(0) + b
Solving for b, we find that b = 1.
Therefore, the rule for the function shown in the table is:
y = 3x + 1
So the answer is B: y = 3x + 1.
What is the function rule for the following situation? Rex paid $20 for a membership to the pool and pays $3.00 each time he goes to the pool.
A. y = 20x + 3
B. 20 = 3x + y
C. y = x + 20
D. none of these
The initial payment of $20 is a one-time cost and the additional $3 fee is paid each time Rex goes to the pool. Let the total cost after x visits to the pool be y.
From the given information, we can see that the $20 membership fee is a fixed cost that does not depend on the number of visits. The cost for the visits, on the other hand, is directly proportional to the number of visits. This means that the function rule is a linear equation of the form:
y = mx + b
where m is the rate of change (the fee per visit) and b is the fixed cost.
In this case, we know that the rate of change is $3 per visit, so m = 3. The fixed cost is the initial payment of $20, so b = 20.
Putting these values into the equation, we get:
y = 3x + 20
Therefore, the function rule for this situation is y = 3x + 20.
So the answer is A: y = 20x + 3.
Find the solution to the system of equations by using either graphing or substitution.
y = 6 – x and y = x – 2
A. (2, 4)
B. (–4, 2)
C. (4, 2)
D. no solutions
We can use substitution to find the solution to the system of equations.
Since both expressions are equal to y, we can set them equal to each other:
6 – x = x – 2
Solving for x, we get:
6 = 2x – 2
8 = 2x
x = 4
Now we can substitute this value of x into either of the original equations to find y:
y = 6 – x = 6 – 4 = 2
Therefore, the solution to the system of equations is (4, 2).
So the answer is C: (4, 2).
y = 2x – 1 and y = x + 3
A. (4, 7)
B. (7, 4)
C. (–7, –4)
D. infinite solutions