The cost of a taxi ride is $5.00 plus $0.75 for every 0.5 km.
Graph this relation
Identify the slope and the vertical intercept of the line. What do the represent?
Write an equation relating the cost and the distance traveled.
I'm not sure how I was supposed to graph this, because normally I make a table of values but I don't know how to make one for this question. Please help, thank you!
C = 5 + 0.75/0.5KM.
C = 5 + 1.50/km
Eq: C = 1.5x + 5.
C = Cost.
Slope = 1.5.
X = Distance traveled.
Y-Intercept = 5.
You have to find the number on the tables first, to graph
Sure, I can help you with that! Let's try to graph the relation and answer the other questions.
To graph the relation, we can use the cost as the dependent variable (y) and the distance traveled as the independent variable (x). We'll make a table of values to plot the points:
Distance (km) | Cost ($)
-------------------------------
0 (initial) | $5.00
0.5 | $5.75
1.0 | $6.50
1.5 | $7.25
2.0 | $8.00
Now, let's plot these points on the graph. The distance traveled (x-axis) will be on the horizontal axis, and the cost (y-axis) will be on the vertical axis. Connect the points to form a straight line.
To identify the slope and vertical intercept of the line, we can use the equation of a straight line in the form: y = mx + b. In this case, 'm' represents the slope, and 'b' represents the vertical intercept.
From the table of values, we can see that for every 0.5 km increase in distance traveled, the cost increases by $0.75. So the slope (m) is $0.75 for every 0.5 km.
The vertical intercept (b) is $5.00, as seen from the initial point (0, $5.00). It represents the fixed cost of $5.00 that you have to pay even if the distance traveled is 0 km.
Now, let's write the equation relating the cost (y) and the distance traveled (x):
y = 0.75x + 5.00
Therefore, the equation relating the cost and the distance traveled is y = 0.75x + 5.00.
To graph this relation, we can use a coordinate plane where the x-axis represents the distance traveled in km, and the y-axis represents the cost in dollars.
To create a table of values for this relation, we can start by choosing some values for the distance traveled and then calculating the corresponding cost.
Let's choose some distances: 0 km, 0.5 km, 1 km, 1.5 km, 2 km, and so on.
For 0 km, the cost would be the base cost of $5.00:
Distance (x) = 0 km, Cost (y) = $5.00.
For 0.5 km, we need to calculate the cost based on the given rate of $0.75 for every 0.5 km:
Distance (x) = 0.5 km, Cost (y) = $5.00 + $0.75 = $5.75.
We can continue this process to find values for other distances:
Distance (x) = 1 km, Cost (y) = $5.00 + 2 * $0.75 = $6.50.
Distance (x) = 1.5 km, Cost (y) = $5.00 + 3 * $0.75 = $7.25.
Distance (x) = 2 km, Cost (y) = $5.00 + 4 * $0.75 = $8.00.
We can repeat this process for more values to get a better understanding of the relation.
Now, with these points, we can plot them on the graph. Each point will represent a specific distance and the corresponding cost. Connect the points to create a line.
The graphed relation should show a straight line increasing as the distance traveled increases. The line will have a positive slope, indicating the rate of $0.75 for every 0.5 km.
The slope of the line represents the rate at which the cost increases per unit of distance. In this case, the slope is $0.75, indicating that the cost increases by $0.75 for every 0.5 km traveled.
The vertical intercept of the line represents the cost when the distance traveled is zero, which is $5.00 in this case. This intercept is the base cost of taking the taxi, regardless of the distance traveled.
To write the equation relating the cost (y) and distance traveled (x), we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the vertical intercept.
Using the values we calculated, the equation becomes:
Cost (y) = $0.75 * Distance (x) + $5.00.
So, the equation relating the cost and the distance traveled is y = 0.75x + 5.