The phone company Splint has a monthly plan where a customer pays a flat monthly fee, and then a set rate per minute. If a customer uses 130 minutes, the monthly cost will be $57. If the customer uses 520 minutes, the monthly cost will be $135. Find the equation of the plan in the form y=mx+b, where x is the number of monthly minutes used and y is the total monthly cost of the Splint plan.

y=

If a customer uses 855 minutes, the total cost will be dollars.

y = 0.2x + 31

855 minutes would cost $202.

Step-by-step explanation:

Let,

a be the cost per minute and f be the flat fee charged.

Now,

130a + f = 57         Eqn 1

520a + f = 135      Eqn 2

Subtracting Eqn 1 from Eqn 2

520a + f - 130a - f = 135 - 57

390a = 78

Dividing both sides by 390

a = $0.2

Putting in Eqn 1

130 (0.2) + f = 57

26 + f = 57

f = 57 - 26

f = 31

Hence the company charges a flat fee of $31 and $0.2 per minute.

Equation in slope intercept form.

y = 0.2x + 31

Now putting x = 855

y = 0.2(855) + 31

y = 171 + 31

y = $202

Therefore,

y = 0.2x + 31

855 minutes would cost $202.

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