12) A new amusement park decides to offer its visitors a choice between two plans. With Plan 1 they pay $6 to enter the park and they pay $3.50 for each ride. With Plan 2 they pay $12 to enter the park and $1.50 for each ride. Write an
equation then find the number of rides when the cost will be the same. What will that cost be?

9514 1404 393

Step-by-step explanation:

The plan 1 cost for x rides will be ...

  y = 6 + 3.50x

The plan 2 cost for x rides will be ...

  y = 12 + 1.50x

These costs will be equal when ...

  y = y

  6 + 3.50x = 12 + 1.50x . . . . . substitute for y

  2.00x = 6 . . . . . . . . . . . . . subtract 6+1.50x

  x = 3 . . . . . . . . . . . . . . . divide by 2

For 3 rides, the cost will be the same.

__

For 3 rides the cost is ...

  y = 6 + 3.50(3) = 6 + 10.50 = 16.50

The cost for 3 rides will be $16.50 for either plan.

it would be 6xy and -16xy.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

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

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form