Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. A solid line, labeled 1, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled 2, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these graphs shows a lower unit cost, 1 or 2
To determine which line has a lower unit cost, we need to compare the slopes of the two lines.
For Line 1, we can calculate the slope using the formula:
slope = (change in y) / (change in x)
slope = (6 - 0) / (3 - 0)
slope = 6/3
slope = 2
For Line 2, we can calculate the slope using the same formula:
slope = (change in y) / (change in x)
slope = (3 - 0) / (6 - 0)
slope = 3/6
slope = 1/2
Comparing the slopes, we see that Line 2 has a lower slope (1/2) compared to Line 1 (2).
Therefore, Line 2 has a lower unit cost.
Use the image to answer the question.
An illustration shows quadrant four of a coordinate plane where the x-axis ranges from 0 to 6 in increments of one and the y-axis ranges from 0 to negative 6 in increments of one. The line passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 4 comma negative 6 right parenthesis.
What is the rate of this graph
To determine the rate of the graph, we need to calculate the slope of the line.
The slope is given by the formula:
slope = (change in y) / (change in x)
In this case, the line passes through the points (0,0) and (4,-6).
So, the change in y is -6 - 0 = -6, and the change in x is 4 - 0 = 4.
Plugging these values into the slope formula, we get:
slope = (-6) / 4 = -3/2
Therefore, the rate of the graph is -3/2.
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled total cost in dollars and the x-axis is titled number of markers. A line is marked on the graph, passing through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 4 comma 3 right parenthesis.
What is the unit cost from the graph
To determine the unit cost from the graph, we need to calculate the slope of the line.
The slope is given by the formula:
slope = (change in y) / (change in x)
In this case, the line passes through the points (0,0) and (4,3).
So, the change in y is 3 - 0 = 3, and the change in x is 4 - 0 = 4.
Plugging these values into the slope formula, we get:
slope = 3 / 4 = 0.75
Therefore, the unit cost from the graph is $0.75.
Question
A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40 for 3 months. You write two equations in the form of y=kx to try and figure out which membership would be cheaper for a year. What is the value of k for the cheaper membership
To determine the value of k for the cheaper membership, we need to set up equations for the cost of each membership and compare their rates.
For Gym A:
The cost for 5 months is $50, so the equation is:
y = kx
50 = 5k
For Gym B:
The cost for 3 months is $40, so the equation is:
y = kx
40 = 3k
To find the value of k for the cheaper membership, we need to solve both equations for k.
For Gym A:
50 = 5k
Dividing both sides by 5, we get k = 10.
For Gym B:
40 = 3k
Dividing both sides by 3, we get k = 40/3 = 13.33 (rounded to 2 decimal places).
Comparing the values of k, we see that k = 10 is smaller than k = 13.33.
Therefore, the value of k for the cheaper membership is 10.
Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y
is the distance in miles and x is the time in hours to represent the motion of the faster car
Let's denote the faster car as "Car A".
For Car A, on Road 1, the car can go 60 miles in 2 hours.
This can be represented by the equation:
y = kx
Substituting the given values, we have:
60 = 2k
Solving for k, we get:
k = 30
Therefore, the equation that represents the motion of the faster car (Car A) is:
y = 30x
Where y represents the distance in miles and x represents the time in hours.
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects is moving at a rate of 2 feet per second