BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.10, Problem 69E

(a)

To determine

To sketch: the graph of the given linear equation.

Expert Solution

Explanation of Solution

The linear equation is given,

y=6x+3000 (1)

Where,

y is the production cost in dollars.

x is the number of toaster ovens which are produced in a month.

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,

0=6x+30006x=3000x=30006=500

The first point on the linear equation is (500,0) .

Substitute 0 for x in equation (1) to find the value of y-intercept,

y=60+3000y=0+3000=3000

The second point on the linear equation is (0,3000) .

The equation (1) is in the form of general equation y=mx+b , so the value of slope m is 6 .

Sketch the graph by the points (500,0) , (0,3000) and the slope m is 6.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.10, Problem 69E

Figure (1)

The graph of linear equation (1) is shown in above Figure (1).

(b)

To determine

The significance of slope and the y- intercept of the graph of the line.

Expert Solution

Explanation of Solution

From part (a), the slope of the linear equation is 6 and the x- intercept is 500 and the y-intercept is 3000.

The slope represents an increase of 6 toaster ovens for each one dollar increase in a month, the y-intercept indicates that 3000 toaster ovens are produced if there is no increase in price, and the x-intercept indicates that no toaster ovens are produced with an decrease of $50 in production cost.

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