Exam 1: Linear Equations and Functions

The equation gives the relation between temperature readings in Celsius and Fahrenheit. If a temperature has reading of -20 Fahrenheit, what is the corresponding reading in Celsius? ​

Write the equation and graph the line that passes through the given point and has the slope indicated. ​ ​(3,3) with 0 slope ​

An advertising agency has found that when it promotes a new product in a city of 350,000 people, the rate of change R of the number of people who are aware of the product is related to the number of people x who are aware of it and is given by , where and Graph this equation with a graphing utility. Based on this graph, is the rate of change increasing or decreasing? ​

A company charting its profits notices that the relationship between the number of units sold x and the profit is linear. If 100 nits sold results in $2,900 profit and 150 units sold results in $6,000 profit. Use these two points on the graph of to find the marginal profit. ​

Choose the equation of the line with the given slope and y-intercept. ​ Slope: y-intercept : ​

Each ounce of substance A supplies 2% of the nutrition a patient needs. Substance B supplies 9% of the required nutrition per ounce, and substance C supplies 6% of the required nutrition per ounce. If digestive restrictions require that substances A and C be given in equal amounts, and the amount of substance B be one-fifth of either of these other amounts, find the number of ounces of each substance that should be in the meal to provide 100% of the required nutrition. ​

Dish Systems manufactures satellite systems and has its monthly profit P in dollars related to the number of satellite systems x by . Find the number of systems that Dish Systems needs to produce and sell in order to break even. ​

Find the slope of the line passing through the given pair of points. ​ and ​

Use a graphing utility with the standard viewing window and to graph the function. Choose the correct graph below. ​ ​

The total price of a new car (including 5% sales tax) is $28,068. How much of this is tax? Round your answer to the nearest cent. ​

A manufacturer of DVD players has monthly fixed costs of $9,000 and variable costs of $70 per unit for one particular model. For this model DVD player, find the function for monthly total costs where x denotes the number of units produced and sold. ​

Suppose a professor counts the final exam as being equal to each of the other tests in her course, and she will also change the lowest test score to match the final exam score if the final exam score is higher. If a student's four test scores are 85, 83, 54, and 95, what is the lowest score the student can earn on the final exam and still obtain at least an 80 average for the course? ​

If , find . ​

Find the slope m and y-intercept b of the line whose equation is given below. ​ Y = -1 ​

Suppose that in a certain market, the demand function for a product is given by and the supply function is given by , where p is the price per unit in dollars and q is the quantity produced. If the government levies a tax of $7 per item on the supplier, who passes the tax on to the consumer as a price increase, find the equilibrium price and quantity after the tax is levied. Round q to the nearest whole number and round p to one decimal place. ​

Use the left-to-right elimination method to solve the system. ​ ​

Use the values in the following table. ​ If the function defined by the table is denoted by f, so that is an input or an output of ? ​

Solve the equation. ​ ​

Determine whether the values in the table describe x as a function of y.

For the given graph, determine whether the line has a slope that is positive, negative, zero, or undefined. ​ ​