Exam 2: Linear Equations and Functions

Retailers will buy 45 cordless phones from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 35 phones at $30 each and 56 at $42 each. Assuming the supply and demand functions are linear, find the market equilibrium point . ​

Find the equilibrium point for the following supply and demand functions below, where p is price per unit and q is the number of units produced and sold. ​ Demand: Supply: ​

Solve for y in terms of x. ​ ​

Find the intercepts of the following function. ​ ​

If and , find and simplify. ​

Suppose that a certain product has the following demand and supply functions, where p is the price per unit in dollars and q is the quantity produced. ​ Demand: Supply: ​ If a $44 tax is placed on each unit of the product of the following. What is the new equilibrium point? ​

The figure below show the demand and supply functions for a product. Decide which line shows the supply function and which line the demand function. ​ ​ Is there a surplus or shortage when the price is $33? ​

Using a graphing utility or Excel to find the solution of the system. ​ ​ ​

​Graph the equation with a graphing utility using the specified range. Is the graph below the graph of the given equation? ​ ​ ​ ​

Let and . Find and simplify. ​

Choose the graph that represents the equation below. ​ ​ ​

Solve the system by elimination, or by any convenient method. ​

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by and , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal? ​

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. ​ ​

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​

Suppose in the figure below. How many values of x satisfy ? ​ ​

Write the equation of the line passing through the given pair of points. ​ (2,-3) and (-1,3) ​

If , is y a function of x?

Solve the system of equations by using graphical methods. ​ ​ ​

As the price of a commodity decreases, what happens to supply? ​