Exam 2: Rates of Change and Linear Functions

Find the slope of the line through the points

Complete the table for the linear function.

Which graph has a slope of ?

Find the equation of the line for the following set of conditions. The slope is -4 and the line passes through the point (3,-6). Write the answer in slope-intercept form, .

The table below gives population figures for Mexico for the period from 1980 to 1986. Population of Mexico: 1980-1986 Find A) by how Find A) by how many millions of people the population has increased from 1980 to 1985 and B) by how many millions of people the population has increased on average each year from 1980 to 1985.

Graph the function

Find the value of y so that the line through the points (9.6,y) and (-5.7,-12.2) has slope 1.

Find the slope of the line shown.

A contractor purchases a piece of equipment for $40,000. The equipment requires an average expenditure of $4.00 per hour for fuel and maintenance, and the operator is paid $13.00 per hour. A) Write an equation giving the total cost C of operating this equipment for the first t hours, including purchasing it. B) Assuming that customers are charged $25.00 per hour of machine use, write an equation for the revenue R derived from t hours of use. C) Use the formula P = R - C to write an equation for the profit, P, derived from the first t hours of use. D) Find the number of hours this equipment must be used to break even, i.e. make a profit of $0. Round your answer to the nearest hour.

In the first 8 years of his career, Hall of Fame baseball player Cal Ripken, Jr., had 1,180 base hits. A) What was his average rate of hits per year for this eight-year period? B) If he continued hitting at this same average rate, how many hits would he accumulate in the first 10 years of his career? C) If he continued hitting at this same average rate, how long would it take him to get to 2,000 hits? Round to the nearest year.

Identify A) the slope and B) the y-intercept.

Determine whether the following data is linear.

The joint plates of a wooden truss require 1 nail for every 40 pounds of stress on the joint. How many nails would be required in a joint that holds 440 pounds of stress?

The graph below displays the population of the Madison, WI by decade. Find: A) The total change from 1940 to 1980. Round answer to the nearest ten-thousand. B) The average rate of change from 1940 to 1980. Round answer to 2 decimal places if necessary.

The number of nails required to hold the joint plates of a truss is directly proportional to the pounds of stress on the joint. If a joint carrying 600 pounds of stress requires 24 nails in the plate, how many nails are required to plate a joint carrying 825 pounds of stress?

Find the equation to describe the data in the table.

Use an estimate of a linear model for this data to extrapolate the requested information. Use points B and E from this table to estimate the slope, and then use point B to estimate the vertical intercept. Round the answers to 2 decimal places. Extrapolate the weekly food expense for a household with 9 children. Round the answer to 2 decimal places.

The amount of weight that can be lifted by a simple machine is directly proportional to the the amount of force applied to the machine. If the machine is able to lift 246 pounds when a force of 41 pounds is applied, how much force would need to be applied in order to lift a weight of 894 pounds?

Write the equation of the line perpendicular to and goes through the point (2, 8).

Find the value of x that satisfies the equation.