0.1 Linear equations: homework  (Page 4/5)

A firm producing computer diskettes has a fixed costs of $10,725, and variable cost of 20 cents a diskette. Find the break-even point if the diskettes sell for $1.50 each.

Whackemhard Sports is planning to introduce a new line of tennis rackets. The fixed costs for the new line are $25,000 and the variable cost of producing each racket is $60. If the racket sells for $80, find the number of rackets that must be sold in order to break even.

Find an equation of the x-axis.

Find the slope of the line whose equation is $\mathrm{2x}+\mathrm{3y}=6$ .

Find the slope of the line whose equation is $y=-\mathrm{3x}+5$ .

Find both the x and y intercepts of the line $\mathrm{3x}-\mathrm{2y}=\text{12}$ .

Find an equation of the line whose slope is 3 and y-intercept 5.

Find an equation of the line whose x-intercept is 2 and y-intercept 3.

Find an equation of the line that has slope 3 and passes through the point (2, 15).

Find an equation of the line that has slope $-\frac{3}{2}$ and passes through the point (4, 3).

Find an equation of the line that passes through the points (0, 32) and (100, 212).

Find an equation of the line that passes through the point (2, 5) and is parallel to the line $y=\mathrm{3x}+4$ .

Find the point of intersection of the lines $\mathrm{2x}-\mathrm{3y}=9$ and $\mathrm{3x}+\mathrm{4y}=5$ .

Is the point (3, – 2) on the line $\mathrm{5x}-\mathrm{2y}=\text{11}$ ?

Find two points on the line given by the parametric equations, $x=2+\mathrm{3t}$ , $y=1-\mathrm{2t}$ .

Find two points on the line $\mathrm{2x}-6=0$ .

Graph the line $\mathrm{2x}-\mathrm{3y}+6=0$ .

Graph the line $y=-\mathrm{2x}+3$ .

A female college student who is 60 inches tall weighs 100 pounds, and another female student who is 66 inches tall weighs 124 pounds. Assuming the relationship between the female students' weights and heights is linear, write an equation giving the relationship between heights and weights of female students, and use this relationship to predict the weight of a female student who is 70 inches tall.

In deep-sea diving, the pressure exerted by water plays a great role in designing underwater equipment. If at a depth of 10 feet there is a pressure of 21 lb/in2, and at a depth of 50 ft there is a pressure of 75 lb/in ² , write an equation giving a relationship between depth and pressure. Use this relationship to predict pressure at a depth of 100 ft.

If the variable cost to manufacture an item is $30, and the fixed costs are $2750, write the cost function.

The variable cost to manufacture an item is $10, and it costs $2,500 to produce 100 items. Write the cost function, and use this function to estimate the cost of manufacturing 300 items.

It costs $2,700 to manufacture 100 items of a product, and $4,200 to manufacture 200 items. If x represents the number of items, and y the costs, find the cost equation, and use this function to predict the cost of 1,000 items.

In 1980, the average house in Palo Alto cost $280,000 and the same house in 1997 costs $450,000. Assuming a linear relationship, write an equation that will give the price of the house in any year, and use this equation to predict the price of a similar house in the year 2010.