A trophy company charges $175 for a trophy plus $0.20 per letter for the engraving. The total charge for a trophy with x letters is given by the function f(x) = 0.20x + 175. How will the graph change if the trophy’s cost is lowered to $172? if the charge per letter is raised to $0.50?

The terms in a linear function consists of the product of a variable raised to the first power and a constant added to a constant

The changes in the graph of the function are;

The reason the above values are correct are given as follows:

The known parameter for the costs of a trophy are;

Amount the company charges for the trophy = $175

Amount charged for each letter written on the trophy - $0.20

The total charge for a trophy with x letters is f(x) = 0.20·x + 175

Required;

The change in the graph if the trophy's cost is lowered to $172

Solution;

The cost of the trophy is the constant term in the straight line equation of the total charge for a trophy

The constant term in a straight line equation gives the y-intercept, that is the value of y when x = 0, while the coefficient of x in the equation of the form y = m·x + c, gives the slope of the equation

Therefore, when the cost of the trophy is lowered to 172, the y-intercept of the graph is lowered to 172, while the slope of the graph remains the same

Required:

The change in the graph if the charge per letter is raised to $0.50

Solution:

The charge per letter is the coefficient of x, in the equation f(x) = 0.20·x + 175, which is of the form, y = m·x + c, where m is the slope

Therefore, the charge per letter is the slope of the graph

If the charge per letter is changed from $0.20 to $0.50, the equation changes from f(x) = 0.20·x + 175 to f(x) = 0.50·x + 175, and therefore;

The slope of the graph changes from 0.20 to 0.50

Learn more about straight line graphs here:

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