The greatest number of people that they may invite and still stay within their budget is 130 people.
The standard form of a linear equation is given by:
y = mx + b
Where y is a dependent variable, x is an independent variable, m is the slope of the line (the rate of change), b is the y intercept (that is the initial value of y).
Let y represent the budget for x number of people.
Since the reception hall charges a $80 cleanup fee plus $34 per person, hence this can be represented by the function:
y = 34x + 80
They have budgeted $4,500 for their reception. Therefore the greatest number of people can be found from:
4500 = 34x + 80
34x = 4420
x = 130 people
Therefore the greatest number of people that they may invite and still stay within their budget is 130 people.
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