Exam 1: Linear Functions

Solve the problem. -Suppose the function y = 4t - 4.5 determines the actual time that has elapsed, in minutes, for t minutes of a person's estimate of the elapsed time. Find the actual time that has elapsed for an Estimate of t = 30 minutes.

Find the slope of the line. - $2 x+4 y=0$

Find the correlation coefficient. -Consider the data points with the following coordinates:

The total number of reported cases of AIDS in the United States has risen from 372 in 1981 to 100,000 in 1989 and 200,000 in 1992. Does a linear equation fit this data? Explain.

Find an equation for the least squares line representing weight, in pounds, as a function of height, in inches, of men. Then, predict the height of a man who is 145 pounds to the nearest tenth of an Inch. The following data are the (height, weight)pairs for 8 men: (66, 150), (68, 160), (69, 166), (70,175), (71, 181), (72, 191), (73, 198), (74, 206).

Evaluate the function as indicated. -Find $f(0)$ when $f(x)=14 x+13$ .

Solve the problem. -Find the temperature at which the Celsius and Fahrenheit scales coincide.

Find an equation in slope-intercept form (where possible) for the line. -The line with y-intercept -10 and perpendicular to x + 2y = 4

Solve the problem. -Northwest Molded molds plastic handles which cost $1.00 per handle to mold. The fixed cost to run the molding machine is $5616 per week. If the company sells the handles for $4.00 each, how many Handles must be molded weekly to break even?

Find an equation in slope-intercept form (where possible) for the line. -Through $(0,-4), \mathrm{m}=\frac{7}{3}$

Solve the problem. -Let the demand and supply functions be represented by $\mathrm{D}(\mathrm{p})$ and $\mathrm{S}(\mathrm{p})$ , where $\mathrm{p}$ is the price in dollars. Find the equilibrium price and equilibrium quantity for the given functions. $\mathrm{D}(\mathrm{p})=134,750-250 \mathrm{p}$ $\mathrm{S}(\mathrm{p})=300 \mathrm{p}$

Find the slope of the line.

Solve the problem. -Suppose that the price and supply for a certain model of graphing calculator are related by $\mathrm{p}=\mathrm{S}(\mathrm{q})=4 \mathrm{q}$ , where $\mathrm{p}$ is the price (in dollars) and $\mathrm{q}$ is the supply (in hundreds) of calculators. Find the supply if the price is $\$ 89$ . Round to the nearest whole number if necessary.

Given the supply and demand functions below, find the price when the demand is $145 .$ $S(p)=9 p+12$ $D(p)=280-9 p$

Find the equation of the least squares line. -Two different tests are designed to measure employee productivity and dexterity. Several employees of a company are randomly selected and asked to complete the tests. The results are Below.

John has been a teacher at West Side High School for the past 12 years. His salary during that time can be modeled by the linear equation y = 800x + 33,000 where x is the number of years since he began teaching at West Side and y is his salary in dollars. Explain what the slope, 800, represents in this context.

Write a cost function for the problem. Assume that the relationship is linear. -A cable TV company charges $21 for the basic service plus $7 for each movie channel. Let C(x)be the total cost in dollars of subscribing to cable TV, using x movie channels.

Evaluate the function as indicated. -Find $f(6.5)$ when $f(x)=-2 x+8.8$ .

Graph the equation. -y = -6

Find an equation in slope-intercept form (where possible) for the line. -Through $(8,-10)$ , parallel to $-5 x+3 y=-46$