Let's break down the questions one by one:
Question 2
a. The constant of proportionality is __________.
(To answer this question, we would generally look at the graph to determine the slope, but since the specifics of the graph are not provided, I cannot generate a numerical answer. Make sure to look at the graph and determine the ratio of y to x when both are positive.)
b. Write an equation that represents this graph __________.
(Again, without the specifics of the graph, I can’t provide a definitive answer. If the graph represents a proportional relationship, it’ll likely be in the form \( y = kx \), where \( k \) is the constant of proportionality.)
c. This is a proportional relationship because the y-intercept is __________.
(For a proportional relationship, the y-intercept should be 0. Hence, you would fill this blank with "0.")
Question 3
The equation of this graph is y = 23x + 2.
What transformation would need to happen for the equation of the line to be y = 23x?
Response:
- Shift the graph down 2.
Question 4
Given the table for x (time in minutes) and y (distance traveled), use the provided data:
| x | 8 | 5 | 7 | 2 | 9 | |----|-----|-----|-----|-----|-----| | y | 664 | 415 | 581 | 166 | 747 |
a. Every minute __________ meters are traveled.
(To find the constant rate, determine the total distance for each time and take the average rate.)
b. Write an equation to show the relationship between x and y: __________.
(Generally, you would look for linear regression or find a proportional relationship based on the averages.)
c. This relationship is __________ because the y-intercept is __________.
(If you identify a direct way these relate, you’d indicate if it’s linear or not; however, if you find that one does not pass through the origin, you’d indicate that it does not have a y-intercept of 0.)
Question 5
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?
Response:
- Charge a flat rate of $20 and then $12 per mile instead of just $12 per mile would change it to a non-proportional situation.
Question 6
One business charges $22 per t-shirt that is custom made. Another business charges $16 per t-shirt plus a $15 setup 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?
Response:
- Down 15 (to account for the $15 setup fee, making the starting cost non-proportional).
Please use the graph data and table information for accurate numerical answers to Questions 2 and 4. Let me know if you have any specific numbers or additional details to share!
2 answers