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? (1 point) Responses No changes are needed. No changes are needed. Charge $15 per mile instead of $12 Charge $15 per mile instead of $12 Charge $4 per mile instead of $12 Charge $4 per mile instead of $12 Charge a flat rate of $20 and then $12 per mile Charge a flat rate of $20 and then $12 per mile Question 6
Charge a flat rate of $20 and then $12 per mile
6. One 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 Up 15 Up 15 Up 4 Up 4 Right 4 Right 4 Down 15 Down 15 Down 4 Down 4 Left 15
Up 15
7. Solve this equation for y: 7y=12x (1 point) Responses y=127x y is equal to 12 sevenths x y=12x+7 y is equal to 12 x plus 7 y=712x y is equal to 7 over 12 x y=12x−7
y=12x/7
13. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. a. What is the rate of change (slope) for this scenario? Response area b. What is the y-intercept for this scenario? c. Write an equation for the scenario in slope-intercept form. d. Write an equation in standard form.
a. The rate of change (slope) for this scenario can be found using the formula:
slope = (change in y) / (change in x)
Given that the water level changed from 60 feet to 45 feet over a period of 3 days, and change in x = 3 days and change in y = 60 - 45 = 15 feet, we can calculate the slope as:
slope = (15 feet) / (3 days) = 5 feet/day
b. The y-intercept for this scenario is the initial water level before the drought began, which is given as 60 feet.
c. To write an equation for the scenario in slope-intercept form (y = mx + b), we can use the slope (m = 5) and the y-intercept (b = 60). The equation is:
y = 5x + 60
d. To write the equation in standard form (Ax + By = C), we can rearrange the equation from slope-intercept form:
y = 5x + 60
-5x + y = 60
So the equation in standard form is:
-5x + y = 60
14. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point)
(y−45)=−5(x−3)
(y+10)=−5(x−10)
(y−3)=−5(x−45)
(y−10)=−5(x+10)
The point-slope equation for the given two points (3, 45) and (10, 10) would be:
(y - 45) = -5(x - 3)
a. Using the graph, describe the key characteristics of the graph (positive/negative slope, proportional/non proportional, y-intercept). b. Write in words what the slope of the graph means in context. c. Write in words what the y-intercept of the graph means in context. d. Write in words what the graph of the line is showing.
a. The graph has a negative slope, as indicated by the coefficient -5 in the equation. It is a proportional graph as it can be represented by a linear equation in point-slope form. The y-intercept is at (3, 45) which means the graph intersects the y-axis at y = 45.
b. The slope of the graph (-5) represents the rate of change in the water level of the river with respect to time. In this context, it means that for every 1 day without rain, the water level decreases by 5 feet.
c. The y-intercept (45) represents the initial water level in the river (before the drought began). It means that when there are 0 days without rain, the water level is 45 feet.
d. The graph of the line shows the relationship between the number of days without rain and the corresponding water level in the river. It visually represents how the water level decreases linearly over time without rain.
a. Using the graph, describe the key characteristics of the graph (positive/negative slope, proportional/non proportional, y-intercept). b. Write in words what the slope of the graph means in context. c. Write in words what the y-intercept of the graph means in context. d. Write in words what the graph of the line is showing.
The graph has (0,10), (10,14), (20,18), (30,22), (50,30) as its points.
a. To describe the key characteristics of the graph, we need to analyze the provided points.
From the given points (0,10), (10,14), (20,18), (30,22), (50,30), we can determine the following characteristics:
- The slope can be determined by calculating the change in y divided by the change in x. From the given points, the slope appears to be positive.
- The graph can be seen as proportional since the points seem to lie on a straight line, indicating a linear relationship.
- The y-intercept can be determined by finding the y-value when x = 0. From the given points, the y-intercept is 10.
b. The slope of the graph represents the rate of change in y (water level) with respect to x (time). In this context, as the slope appears to be positive, it means that as time increases, the water level also increases. The exact rate of change can be calculated using the given points.
c. The y-intercept of the graph represents the initial water level at the start, when x = 0. In this context, the y-intercept of 10 means that at the beginning (time = 0), the water level was 10.
d. The graph of the line represents the relationship between time (x-axis) and the corresponding water level (y-axis). It shows how the water level changes over time.