Question

Part A: Abe rented a bike at $36 for 5 days. If he rents the same bike for 8 days, he has to pay a total rent of $48.

Answer 1

Answer:

Equation of the system is y = 4x + 16 and in function form is f(x) = 4x + 16.

Step-by-step explanation:

A. We are given that, the rent for 5 days is $36 and for 8 days is $48 i.e. in the tuple form we get the points (x,y) = (5,36) and (8,48) where x= no. of days for which the bike is rented and y= rent in dollars.

Now, using these two points we will find the slope 'm' of the function.

i.e. m = $\frac{48-36}{8-5}$

i.e. m = 4.

Now, the general form of the straight line is y = mx + b, where b is the y-intercept.

Using the point (x,y) = (5,36) and slope m = 4, we will find the value of 'b' by substitution.

i.e. 36 = 4*5 + b  i.e  b = 16

Hence, the equation of the system is y = 4x + 16.

B. We have to write y = 4x + 16 into function notation i.e. f(x) = y

Hence, function notation is f(x) = 4x + 16.

C. Let x-axis be the number of days for which bike is rented and y-axis be the rent in dollars. Let the intervals be 1 unit apart.

Now, we can find the end points (0,16) and (-4,0). Plot these points and join them, this will give you the graph of the equation as shown below.

Answer 2

(5,36)(8,48)
slope = (48 - 36) / (8 - 5) = 12/3 = 4

y = mx + b
slope(m) = 4
(5,36)...x = 5 and y = 36
now sub and find b
36 = 4(5) + b
36 = 20 + b
36 - 20 = b
16 = b

equation is : y = 4x + 16.....in standard form : 4x - y = -16 <==
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function notation : f(x) = 4x + 16
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x axis will be ur hrs....I would label them at intervals of 1
y axis will be total cost of renting the bike......as far as the intervals...not sure how to label them.....sorry....I wanna say intervals of 2...but am not sure

y = 4x + 16
slope = 4
y int = (0,16)
x int = (-4,0)

so start at (-4,0)....and since ur slope is 4, go up 4 and to the right 1...keep doing this and u will cross the y axis at (0,16)