Answer
a) Option A
y = 2x + 10
Option B
y = 3x
b) Option A is represented with the red line and Option B is represented by the blue line.
Total Cost is presented on the y-axis and the Number of rides is presented on the x-axis.
The graph is presented below.
From this graph, we can see that the two lines cross at (10, 30)
So, the two options will have the same rides and the same total cost when
x = 10 rides
y = 30 dollars
Step-by-step explanation
There are two options to consider,
Let the amount to be paid be y
Let the number of rides be x
Option A
Each ride costs $2
x rides will cost 2x dollars
Activation fee = 10 dollars
Total cost = y
y = 2x + 10
Option B
Each ride costs $3
x rides will cost 3x dollars
Activation fee = 0
Total cost = y
y = 3x
So, we end up with a system of equation for when the number of rides and the total cost for both options become the same
y = 2x + 10
y = 3x
b) We are asked to solve this system of equations by graphing.
To do this, we will first plot the two lines for each equation, then the solution will be where the two lines cross each other.
We will use intercepts to plot the first line
y = 2x + 10
when x = 0,
y = 2x + 10
y = 2(0) + 10
y = 0 + 10
y = 10
First point on this line is (0, 10)
when y = 0
y = 2x + 10
0 = 2x + 10
-2x = 10
Divide both sides by -2
(-2x/2) = (10/-2)
x = -5
Second point on the line is (-5, 0)
For the second option
y = 3x
when x = 0
y = 3x
y = 3(0)
y = 0
First point on this line is (0, 0)
when x = 1
y = 3x
y = 3(1) = 3
Second point on the line is (1, 3)
We will now plot each of the lines by connecting each of the two points obtained for each line.
Hope this Helps!!!