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.