Exam 1: Linear Equations and Graphs

Solve the problem. -A piece of equipment was purchased by a company for $10,000 and is assumed to have a salvage value of $3,000 in 10 years.If its value is depreciated linearly from $10,000 to $3,000,find a linear equation in the form V = mt + b,t time in years,that will give the salvage value at any time t,0 c t c 10.

Determine whether the slope of the line is positive, negative, zero, or undefined. -

Solve the problem. -The mathematical model C = 600 x + 30,000 represents the cost in dollars a company has in manufacturing x items during a month.Using this model,how much does it cost to produce 600 items?

Provide an appropriate response. -Write the equation of the line in the following graph.

Find the slope and y intercept of the graph of the equation. -y= +

Provide an appropriate response. -Find the standard form of the equation of the line with slope of and passing through (4,4).

Solve the problem. -The cost of manufacturing a computer part is related to the quantity produced,x,during a production run. When 100 parts are produced,the cost is $300.When 600 parts are produced,the cost is $4800.Find an equation Of the line relating quantity produced to cost.Write the final answer in the form C = mx + b.

Solve the problem. -At a local grocery store the demand for ground beef is approximately 50 pounds per week when the price per pound is $4,but is only 40 pounds per week when the price rises to $5.50 per pound.Assuming a linear relationship between the demand x and the price per pound p,express the price as a function of demand.Use this model to predict the demand if the price rises to $5.80 per pound.

Solve the problem. -Suppose the sales of a particular brand of MP3 player satisfy the relationship S = 200x + 3800,where S represents the number of sales in year x,with x = 0 corresponding to 2002 .Find the number of sales in 2005.

Provide an appropriate response. -Write the equation of a line that passes through (3,9)and (0,-7).Write the final answer in the form Ax + By = C where A,B,and C are integers with no common divisors (other than ±1)and A > 0.

Solve the inequality and graph. Express your answer in interval notation. --4(-2 - x)< 6x + 19 - 11 - 2x

Provide an appropriate response. -Find the standard form of the equation of the line passing through the two points.(2,- 6)and (- 9,6)

Provide an appropriate response. -Find the line passing through the two points.Write the equation in standard form.(-3,6)and (6,6)

Solve the problem. -Using a phone card to make a long distance call costs a flat fee of $0.85 plus per $0.19 minute starting with the first minute.Find the total cost of a phone call which lasts 8 minutes.

Find the slope and y intercept of the graph of the equation. -y=

Use the graph to find the average rate of change. -

Provide an appropriate response. -Use the graph to find the slope,x-intercept and y-intercept of the line.

Solve the problem. -Assume that the price per unit d of a certain item to the consumer is given by the equation d = 35 - .10x,where x is the number of units in demand.The price per unit from the supplier is given by the equation s = .2x + 20,where x is the number of units supplied.Find the equilibrium price and the equilibrium quantity.

Solve the formula for the specified variable. -7x + 10y = 19 for y

Solve the formula for the specified variable. -S = for h