91Ó°ÊÓ

Forensic scientists use the lengths of certain bones to calculate the height of a person. Two such bones are the tibia \((t),\) the bone from the ankle to the knee, and the femur \((r),\) the bone from the knee to the hip socket. A person's height \((h)\) in centimeters is determined from the lengths of these bones using the following functions. For men: \(\quad h(r)=69.09+2.24 r\) or \(\quad h(t)=81.69+2.39 t\) For women: \(\quad h(r)=61.41+2.32 r\) or \(h(t)=72.57+2.53 t\) (a) Find the height of a man with a femur measuring \(56 \mathrm{~cm}\). (b) Find the height of a man with a tibia measuring \(40 \mathrm{~cm} .\) (c) Find the height of a woman with a femur measuring \(50 \mathrm{~cm}\). (d) Find the height of a woman with a tibia measuring \(36 \mathrm{~cm}\).

If a line has slope \(0.2,\) then any line parallel to it has slope _________ , and any line perpendicular to it has slope _______ .

Determine whether each pair of lines is parallel, perpendicular, or neither. The line passing through (15,9) and (12,-7) and the line passing through (8,-4) and (5,-20)

Write an equation in the form \(y=m x\) for each situation. Then give the three ordered pairs associated with the equation for \(x\) -values \(0,5,\) and \(10 .\) See Example \(7(a) .\) \(x\) represents the number of gallons of gas sold at \(\$ 3.75\) per gal, and \(y\) represents the total cost of the gasoline (in dollars).

Write an equation in the form \(y=m x\) for each situation. Then give the three ordered pairs associated with the equation for \(x\) -values \(0,5,\) and \(10 .\) See Example \(7(a) .\) \(x\) represents the number of tickets to a performance of Hamilton purchased at \(\$ 250\) per ticket, and \(y\) represents the total paid for the tickets (in dollars).

Determine whether each pair of lines is parallel, perpendicular, or neither. \(x=6\) and \(6-x=8\)

The upper deck at Guaranteed Rate Field in Chicago has produced, among other complaints, displeasure with its steepness. It is \(160 \mathrm{ft}\) from home plate to the front of the upper deck and \(250 \mathrm{ft}\) from home plate to the back. The top of the upper deck is \(63 \mathrm{ft}\) above the bottom. What is its slope?

The average price of a movie ticket in 2004 was \(\$ 6.21 .\) In \(2016,\) the average price was \(\$ 8.65 .\) Find and interpret the average rate of change in the price of a movie ticket per year to the nearest cent.

Three points that lie on the same straight line are said to be collinear. Consider the points \(A(3,1), B(6,2),\) and \(C(9,3) .\) Find the slope of segment \(A C\).

Three points that lie on the same straight line are said to be collinear. Consider the points \(A(3,1), B(6,2),\) and \(C(9,3) .\) Use the slope formula to determine whether the points \((1,-2),(3,-1),\) and (5,0) are collinear.