Use the graph the answer the following questions. (3 points) a. The constant of proportionality is . b. Write an equation that represents this graph . c. This is a proportional relationship because the y-intercept is
the graph is a small graph that goes to 8 on the x axis and 70 on the y axis the y axis is income the x axis is hours
the graph starts at zero and it ends at
(5, 70)
a. The constant of proportionality is the ratio of the change in y to the change in x. From the information given, we can see that the change in y (income) is 70 - 0 = 70, and the change in x (hours) is 5 - 0 = 5. Therefore, the constant of proportionality is 70/5 = 14.
b. Since the relationship is proportional, we can write the equation as y = kx, where k is the constant of proportionality. From part a, we found that k = 14, so the equation that represents this graph is y = 14x.
c. Since the graph starts at y = 0 when x = 0, the y-intercept is 0.
it actually ends at (5, 75)
Oops, I apologize for the misunderstanding. If the graph ends at (5, 75), then the change in y (income) is 75 - 0 = 75, and the change in x (hours) is 5 - 0 = 5. Therefore, the constant of proportionality is 75/5 = 15.
The equation that represents this graph is y = 15x.
Since the graph starts at y = 0 when x = 0 and ends at (5, 75), the y-intercept is still 0.
3. The equation of this graph is y=2/3x+2 What transformation would need to happen for the equation of the line to be y=2/3x ? (1 point) Responses Shift the graph right 3, down 2 Shift the graph right 3, down 2 Shift the graph left 2 Shift the graph left 2 Shift the graph down 3, left 2 Shift the graph down 3, left 2 Shift the graph down 2
To transform the equation from y = (2/3)x + 2 to y = (2/3)x, we need to shift the graph down by 2 units. This can be achieved by subtracting 2 from the original equation.
Therefore, the correct transformation is to shift the graph down 2.
4. Given the table for x, time in minutes, and y, distance traveled: x: time 8 5 7 2 9 y: distance 664 415 581 166 747 (4 points) a. Every minute meters are traveled. b. Write an equation to show the relationship between x and y: . c. This relationship is because the y-intercept is
a. To find the rate at which meters are traveled per minute, we need to calculate the change in distance divided by the change in time for any two points. Let's take the first two points (8, 664) and (5, 415):
Change in distance = 664 - 415 = 249 meters
Change in time = 8 - 5 = 3 minutes
Therefore, meters traveled per minute = 249 / 3 = 83 meters.
b. To write an equation showing the relationship between x (time) and y (distance traveled), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use any two points from the table.
Let's take the first two points (8, 664) and (5, 415) again:
Slope (m) = (415 - 664) / (5 - 8) = -249 / -3 = 83
Thus, the equation that represents the relationship between x and y is:
y = 83x + b
c. Looking at the table, we see that the y-intercept is 664 when x = 8. So, the relationship is because the y-intercept is 664.
is it proportional or no
To determine if the relationship between x and y is proportional, we need to check if the ratio between y and x remains constant for all the data points.
Let's calculate the ratios for each data point:
(8, 664): 664/8 = 83
(5, 415): 415/5 = 83
(7, 581): 581/7 = 83
(2, 166): 166/2 = 83
(9, 747): 747/9 = 83
Since the ratio y/x is the same (83) for all the data points, we can conclude that the relationship between x and y in this table is indeed proportional.
. A cab company charges $12 per mile for a lift to the airport. What change would the company make to their charges to make this a non proportional situation? (1 point) Responses No changes are needed. No changes are needed. Charge a flat rate of $20 and then $12 per mile Charge a flat rate of $20 and then $12 per mile Charge $4 per mile instead of $12 Charge $4 per mile instead of $12 Charge $15 per mile instead of $12
To make this a non-proportional situation, the company would need to make a change to their charges by implementing a flat rate in addition to the per mile charge.
In the given options, the correct choice is to "Charge a flat rate of $20 and then $12 per mile". By adding a flat rate of $20 in addition to the $12 per mile charge, the total cost would depend on the distance traveled, but it would no longer be a constant rate per mile, making it a non-proportional situation.
ne business charges $22 per t-shirt that is custom made. Another business charges $16 per t-shirt plus a $15 set up fee for custom made t-shirts. How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph? (1 point) Responses Left 15 Left 15 Up 15 Up 15 Down 15 Down 15 Down 4 Down 4 Up 4 Up 4 Right 4 Right 4
To transform the first graph to make it become a non-proportional graph with the same y-intercept as the second graph, we would need to decrease the slope (rate) of the first graph.
Since the y-intercept remains the same, we only need to focus on changing the slope. We can achieve this by decreasing the rate at which the cost increases.
Looking at the information provided, the first business charges $22 per t-shirt with no additional fees. The second business charges $16 per t-shirt plus a $15 set-up fee. To achieve a similar non-proportional situation with the same y-intercept, we can consider charging a higher flat fee in addition to the $22 per t-shirt.
Therefore, the intended transformation would be to "Up 15". By adding a flat fee of $15 to the original price of $22 per t-shirt, we would have a non-proportional situation with the same y-intercept as the second graph.