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Concept explainers
Flea Market The manager of a weekend flea market knows from past experience that if she charges x dollars for a rental space at the flea market, then the number y of spaces she can rent is given by the equation y = 200 − 4x.
- (a) Sketch a graph of this linear equation. (Remember that the rental charge per space and the number of spaces rented must both be nonnegative quantities.)
- (b) What do the slope, the y-intercept, and the x-intercept of die graph represent?
(a)
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To sketch: the graph of the given linear equation.
Explanation of Solution
The linear equation is given,
Where,
y is the number of spaces that manager can rent.
x is the charges for a rental space in dollars.
Calculate x-intercept and y-intercept of line to find the two points of the linear equation that represents a line,
Substitute 0 for y in equation (1) to find the value of x-intercept,
The first point on the linear equation is
Substitute 0 for x in equation (1) to find the value of y-intercept,
The second point on the linear equation is
The equation (1) is in the form of general equation
Sketch the graph by the points
Figure (1)
The graph of linear equation (1) is shown in above Figure (1).
(b)
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The significance of slope and the y- intercept of the graph of the line.
Explanation of Solution
From part (a), the slope of the linear equation is
The slope represents a decrease of 4 spaces rented for each one dollar increase in rental price, the y-intercept indicates that 200 spaces are rented if there is no increase in price, and the x-intercept indicates that no space are rented with an increase of $50 in rental price.
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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