Chapter 1, Problem 28RPS

Use the following graph to answer the following question:

1. (a) What is the value of x when y=4.0?
2. (b) What is the value of y when x = 3.0?
3. (c) What are the slope and the y-intercept of the line?
4. (d) What is the value of y when x= 1.0?

Interpretation Introduction

Interpretation: The unknown values using the graph to be predicted.

Concept Introduction:

Graph and graphing: In the equation,$y=\text{m }x+b$ where y is referred as dependent variable, x is called the independent variable, and m is the slope of the line.

Answer to Problem 28RPS

The value of x is $0.2$

Explanation of Solution

The value of $\text{x}$ is calculated as,

  $\begin{array}{l}\text{Consider}\text{two points: (0}\text{.05,1}{\text{.0) as (x}}_{\text{1}},{\text{y}}_1{\text{) and (0,0) as (x}}_{\text{2}},{\text{y}}_{\text{2}}\text{)}\\ \text{slope:}\frac{{\text{x-x}}_{\text{1}}}{{\text{y-y}}_{\text{1}}}\text{=}\frac{{\text{x}}_{\text{1}}{\text{-x}}_{\text{2}}}{{\text{y}}_{\text{1}}{\text{-y}}_{\text{2}}}\\ \frac{\text{x - 0}\text{.05}}{\text{y -1}\text{.0}}\text{ = }\frac{\text{0}\text{.05 - 0}}{\text{1}\text{.0 - 0}}\\ \frac{\text{x - 0}\text{.05}}{\text{y - 1}\text{.0}}\text{=}\frac{\text{0}\text{.05}}{\text{1}\text{.0}}\\ \text{x - 0}\text{.05 (1}\text{.0) = 0}\text{.05 }\left(\text{y-1}\text{.0}\right)\\ \text{ x - 0}\text{.05 = 0}\text{.05 y - 0}\text{.05}\\ \text{x- 0}\text{.05 y = 0}\\ \text{when y = 4}\text{.0 ,}\\ \text{x = 0}\text{.05 (4}\text{.0) = 0}\text{.2}\\ \boxed{\text{x = 0}\text{.2}}\end{array}$

From the given details, the values are calculated as shown above.

Interpretation Introduction

Interpretation: The unknown values using the graph to be predicted.

Concept Introduction:

Graph and graphing: In the equation,$y=\text{m }x+b$ where y is referred as dependent variable, x is called the independent variable, and m is the slope of the line.

Answer to Problem 28RPS

The value of y is $6$

Explanation of Solution

  $\begin{array}{l}\text{Consider}\text{two points: (0}\text{.05,1}{\text{.0) as (x}}_{\text{1}},{\text{y}}_1{\text{) and (0,0) as (x}}_{\text{2}},{\text{y}}_{\text{2}}\text{)}\\ \text{slope:}\frac{{\text{x-x}}_{\text{1}}}{{\text{y-y}}_{\text{1}}}\text{=}\frac{{\text{x}}_{\text{1}}{\text{-x}}_{\text{2}}}{{\text{y}}_{\text{1}}{\text{-y}}_{\text{2}}}\\ \frac{\text{x - 0}\text{.05}}{\text{y -1}\text{.0}}\text{ = }\frac{\text{0}\text{.05 - 0}}{\text{1}\text{.0 - 0}}\\ \frac{\text{x - 0}\text{.05}}{\text{y - 1}\text{.0}}\text{=}\frac{\text{0}\text{.05}}{\text{1}\text{.0}}\\ \text{x - 0}\text{.05 (1}\text{.0) = 0}\text{.05 }\left(\text{y-1}\text{.0}\right)\\ \text{ x - 0}\text{.05 = 0}\text{.05 y - 0}\text{.05}\\ \text{x- 0}\text{.05 y = 0}\\ \text{when x = 0}\text{.30 ,}\\ \text{0}\text{.30 - 0}\text{.05 y = 0}\\ \text{y = }\frac{\text{0}\text{.30}}{0.05}\text{ = 6}\\ \boxed{\text{y = 6}}\end{array}$

From the given details, the values are calculated as shown above.

Interpretation Introduction

Interpretation: The unknown values using the graph to be predicted.

Concept Introduction:

Graph and graphing: In the equation,$y=\text{m }x+b$ where y is referred as dependent variable, x is called the independent variable, and m is the slope of the line.

Answer to Problem 28RPS

The value of slope is $0.052$ and y-intercept is $y=0$

Explanation of Solution

  $\begin{array}{l}\text{Consider}\text{two points: (0}\text{.25,4}{\text{.5) as (x}}_{\text{1}}{\text{,y}}_{\text{1}}\text{) and (0}\text{.38,7}{\text{.0) as (x}}_{\text{2}}{\text{,y}}_{\text{2}}\text{)}\\ \text{slope : m = }\frac{{\text{x}}_{\text{2}}{\text{-x}}_{\text{1}}}{{\text{y}}_{\text{2}}{\text{-y}}_{\text{1}}}\\ \text{ =}\frac{\text{0}\text{.38}\text{- 0}\text{.25}}{\text{7}\text{.0}\text{- 4}\text{.5}}\\ \text{ =}\frac{\text{0}\text{.13}}{\text{2}\text{.5}}\\ \text{m = 0}\text{.052}\end{array}$

At x= 0,

  $\begin{array}{l}\text{x- 0}\text{.05 y = 0}\\ \text{when x = 0 ,}\\ \text{y = 0}\end{array}$

From the given details, the values are calculated as shown above.

Interpretation Introduction

Interpretation: The unknown values using the graph to be predicted.

Concept Introduction:

Graph and graphing: In the equation,$y=\text{m }x+b$ where y is referred as dependent variable, x is called the independent variable, and m is the slope of the line.

Answer to Problem 28RPS

The value of y is $20$

Explanation of Solution

  $\begin{array}{l}\text{Consider}\text{two points: (0}\text{.05,1}{\text{.0) as (x}}_{\text{1}},{\text{y}}_1{\text{) and (0,0) as (x}}_{\text{2}},{\text{y}}_{\text{2}}\text{)}\\ \text{slope:}\frac{{\text{x-x}}_{\text{1}}}{{\text{y-y}}_{\text{1}}}\text{=}\frac{{\text{x}}_{\text{1}}{\text{-x}}_{\text{2}}}{{\text{y}}_{\text{1}}{\text{-y}}_{\text{2}}}\\ \frac{\text{x - 0}\text{.05}}{\text{y -1}\text{.0}}\text{ = }\frac{\text{0}\text{.05 - 0}}{\text{1}\text{.0 - 0}}\\ \frac{\text{x - 0}\text{.05}}{\text{y - 1}\text{.0}}\text{=}\frac{\text{0}\text{.05}}{\text{1}\text{.0}}\\ \text{x - 0}\text{.05 (1}\text{.0) = 0}\text{.05 }\left(\text{y-1}\text{.0}\right)\\ \text{ x - 0}\text{.05 = 0}\text{.05 y - 0}\text{.05}\\ \text{x- 0}\text{.05 y = 0}\\ \text{when x = 1}\text{.0 ,}\\ \text{1}\text{.0 - 0}\text{.05 y = 0}\\ \text{y = }\frac{\text{1}\text{.0}}{0.05}\text{ = 20}\\ \boxed{\text{y = 20}}\end{array}$

From the given details, the values are calculated as shown above.