Question

here is the graph of a function showing the amount of money remaining on a subway fare card as a function of the number of rides taken. please look at the picture to help answer the questions.

Answer 1

Explanation:

This is a linear graph,

Let find the equation of the line

Equation of a line can be determine using

y = mx + c

Where m Is the slope of the graph and c is the intercept on y axis when x = 0

So,

Slope m can be calculated using

Let chose the two point on the x and y axis

P1 = (0,45) and , P2 = (18,0)

m = ∆y / ∆x = y2 - y1 / x2 - x1

m = 0 - 45 / 18 - 0

m = -45 / 18

m = -2.5

So, the intercept on the y axis when x = 0 is 45. Then, c = 45

So, the equation of the line becomes

y = -2.5x + 45

Multiply through by 2

2y = -5x + 90

Where

y is dollars on card, = output

x is the number of rides = input

A. So, we want to find the output when the input is 10, I.e when x = 10

Then,

y = -2.5x + 45

x = 10

y = -2.5 × 10 + 45

y = -25 + 45

y = 20

Then, the output is 20 dollars on card.

B. When the output is 5

I.e y = 5

Then,

y = -2.5x + 45

5 = -2.5x + 45

5-45 = -2.5x

-40 = -2.5x

x = -40 / -2.5

x = 16 rides

The input is 16 number of rides

C. Point P is (7,27.5)

This tells us that when the input is 7, I.e the number of rides is 7, then, the output is 27.5 I.e their are $27.5 dollars on card.