Question

part A Max rented a motor bike at $465 for 5 days if he rents the same motor bike for a week he has to pay a total rent of $625 write an equation in the standard form to represent the total rent (Y) that max has to pay for renting the motorbike for x days part b write the equation obtained in Part A using function notation part c describe the steps to graph the equation obtained above on the coordinate axis. mention the labels on the axes and the intervals

Answer 1

(5,465)(7,625)

slope(m) = (625 - 465) / (7 - 5) = 160/2 = 80

y = mx + b

slope(m) = 80

use either of ur points (5,465)...x = 5 and y = 465

now we sub and find b, the y int

465 = 80(5) + b

465 = 400 + b

465 - 400 = b

65 = b

equation is : y = 80x + 65...but we need it in standard form

y = 80x + 65

-80x + y = 65...multiply by -1 to make x positive

80x - y = -65 <== standard form

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function notation.....f(x) is the same as y

so y = 80x + 65 in function notation becomes f(x) = 80x + 65

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x axis will be days rented

y axis will be total cost

to graph :

y = 80x + 65.....the slope here is 80...the y int is (0,65)

to find the x int, sub in 0 for y and solve for x

0 = 80x + 65

-80x = 65

x = - 65/80 = - 13/16....so ur x int is (-13/16,0)

and if u need to find more points on ur line....

80x - y = -65....sub in any number for x, and solve for y

Answer 2

If Max rented the bike for 5 days and paid $465, we can take this as the first point (5, 465)

And whe he rented the bike for a week, 7 days, he paid $625, so we can take this as the seond point (7, 625)

Now, we will get the line equation based on this two points

First we have to find out the slope:

m = (y2 - y1)/(x2 -x1) = (625 - 465)/(7 - 5) = 1`60/2 = 80

So the slope m = 80

Now using the general formula of a line y = mx + b and the first point, we will find the value of b

y = mx + b

465 = 80(5) + b

465 = 400 + b

465 - 400 = b

65 = b

So b is 65

part a)

Then the line equation y = mx + b, in this case is: y = 80x + 65

part b)

f(x) = 80x + 65

part c)

The x axis is days and the y axis is dollars