Question

PLEASE HELP!! 100 POINTS

Answer 1

see explanation

Explanation:

the total cost is dependent on the number of rides she takes, then

the number of rides is the independent variable and the total cost is the dependent variable.

----------------------------------------------------------------------------

(2)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (- 4, 2 ) into the partial equation

2 = - 2(- 4) + c = 8 + c ( subtract 8 from both sides )

- 6 = c

y = - 2x - 6 ← equation of line

--------------------------------------------------------------------------

(3)

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, 6 ) and (x₂, y₂ ) = (9, - 2 )

m =
`(-2-6)/(9-(-3))` =
`(-8)/(9+3)` =
`(-8)/(12)` = -
`(2)/(3)` , then

y = -
`(2)/(3)` x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (9, - 2 )

- 2 = -
`(2)/(3)` (9) + c = - 6 + c ( add 6 to both sides )

4 = c

y = -
`(2)/(3)` x + 4 ← in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 2x + 12 ( add 2x to both sides )

2x + 3y = 12 ← equation in standard form

----------------------------------------------------------------------------

(4)

linear function has the form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, 200) and (x₂, y₂ ) = (2, 500) ← 2 ordered pairs from the table

m =
`(500-200)/(2-0)` =
`(300)/(2)` = 150

the ordered pair (0, 200 ) indicates that c = 200

y = 150x + 200 ← linear equation

--------------------------------------------------------------------------

(5)

money left over f(x) is

f(x) = initial amount - expenses

= 125 - (15 + 40 + 5x)

= 125 - (55 + 5x)

= 125 - 55 - 5x

= 70 - 5x

that is

f(x) = - 5x + 70