Q. 4.97 The equation h=2s+50聽is used to... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 4: Q. 4.97 (page 509)

The equation $h = 2 s + 50$ is used to estimate a woman鈥檚 height in inches, $h$ , based on her shoe size, $s$ .
鈸� Estimate the height of a child who wears women鈥檚 shoe size $0$ .
鈸� Estimate the height of a woman with shoe size $8$ .
鈸� Interpret the slope and h-intercept of the equation.
鈸� Graph the equation.

Short Answer

Expert verified

Part 鈸� Height of a child who wears women's shoe size $0$ is: $50$ inches

Part 鈸� Height of a woman with shoe size $8$ is: $66$ inches

Part 鈸� The slope, $m = 2$ , means that when the shoe size increases by an inch, height of the woman increases by $2$ inches. The h-intercept means that estimated height of the woman is $50$ inches when shoe size is $0$ .

Part 鈸� Graph of the equation

Step by step solution

Part (a) Step 1. Given Information

The equation $h = 2 s + 50$ is used to estimate a woman鈥檚 height in inches, $h$ , based on her shoe size, $s$ .

Part (a) Step 2. Estimating the height of a child who wears women’s shoe size 0

Put $s = 0$ in the given equation $h = 2 s + 50$

鈬� h = 2 (0) + 50 鈬� h = 0 + 50 鈬� h = 50

Part (b) Step 1. Estimating the height of a woman with shoe size 8

Put $s = 8$ in the given equation $h = 2 s + 50$

鈬� h = 2 (8) + 50 鈬� h = 16 + 50 鈬� h = 66

Part (c) Step 1. Interpreting the slope and h-intercept of the equation

The equation $h = 2 s + 50$ is in slope-intercept form $y = m x + b$ .

By comparison, we get, slope, $m = 2$ ,which means that with increase in shoe size by an inch, height of woman increases by $2$ inches. h-intercept means that estimated height of woman is $50$ inches when shoe size is $0$ .

Part (d) Step 1. Graphing the equation

Graphing the equation $h = 2 s + 50$

Start at the h-intercept $(0, 50)$ , and then count out the rise of $2$ and the run of $1$ to get a second point $(1, 52)$ as shown in the graph and join the points to get the required line.