The student council is planning a dance for their high school They did some research and found that the relationship between the ticket price and income that they will receive from the dance can be modeled by the function They also calculated their expenses and found that their expenses can be modeled by the function 10 . What ticket price ( s ) could the student council charge for the dance if they wanted to break - even ( the expenses are equal to the income ) ? f(x)=-100(x-3)^ 2 +1500,

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

.95

step-by-step explanation: