4.4 1. y varies inversely with the cube of x . If y=375 when x=15, find y when x=12. Y=? 2. The temperature of a gas varies directly with its pressure. A temperature of 200 K produces a pressure of 50 pounds per square inch. a. Find the equation that relates pressure to temperature (Use T for temperature, and P for pressure). = ? 4.1 1. For the function: f(x)=5x 2 +9 , find a. f(x)f(a)xa = b. f(x+h)f(x)h = 2. Find the slope of any line parallel to the line through (1,6) and (3,5) . Slope = 4.2 1. Give the equation of the line with the following slope and y intercept. m=1 , b=3/4 y= Find the equation of the line that passes through the two points (1,1/5 ) and (1/4 ,1/4 ) . Write your answer in standard form. 2. Graph each of the following lines. In each case, name the slope, the x intercept, and the y intercept. a. y=1/3 x b. x=3 c. y=4 a. Slope: = x -intercept: ( ,0) = y -intercept: (0, ) = b. Slope: = x -intercept: ( ,0) = y -intercept: (0, ) = c. Slope: = x -intercept: ( ,0) = y -intercept: (0, ) = 3. Find the equation of the line parallel to the graph of 4x+3y=2 that contains the point (2,4) . 4.3 1. A trained cyclist pedals faster as he increases his cycling speed, even with a mulitple-gear bike. The table shows the pedal frequency, p (in revolutions per minute), and the cycling speed, c (in kilometers per hour), of one cyclist. a. Plot the data and draw a line of best fit through the data points. Clear All Draw: b. Estimate the cyclist's pedal frequency at a speed of 20 km/hr. revolutions per minute = c. Estimate the cyclist's speed when he is pedaling at 90 revolutions per minute km/hour = 2. Birds' nests are always in danger from predators. If there are other nests close by, the chances of predators finding the nest increase. The table shows the probability of a nest being found by predators and the distance to the nearest neighboring nest. a. Plot the data and draw a line of best fit through the data points. Does it look like someone made an error? Ignoring the incorrect data point, draw a line of best fit through the other points. b. Use the regression line to estimate the probability of predators finding a nest if its nearest neighbor is 80 meters away. % = c. If the probability of predators finding a nest is 30% , how far away is its nearest neighbor? Meters = d. What is the probability of predators finding a nest if its nearest neighbor is 140 meters away? %=