Ch. P Applying Linear Equations in Two Variables

CH P Applying Linear Equations in Two Variables

Option 4 - Chapter Opener Problem - The Speed of Light p36
Planet: Uranus

1. The first thing I did was replace the word problem with Uranus and gathered the required information from google.com.

2. I used the equation formulas that the book used in their problems: t=a/r, d=rxt, and d=rxt.

3. In all of the problems I simply plugged the numbers in: distance, rate, and time.

4. Then I solved after changing all the numbers into scientific form and got my solutions.

5. I also drew a picture to show my solutions.

Ch P: How to do Applying Linear Functions in Two Variables

Chapter P Opener Problem Part C
Option 4

First, I have to search online to find the light speed from Earth to Jupiter.
After I found the light speed from earth to Jupiter, I formed a question that I need to solve: Approximate the distance between Earth and Jupiter.

The Procedures:
1) I used the linear equation d = r times t (distance equals rate times time). First, I found the values of r and t, not d, because I'm trying to find d.

r = 186,000 miles/second
t = 34.98 minutes
d = ?

2) Then, I converted 34.98 minutes to seconds to keep the units the same. I multiply 60 and 34.98 minutes and got 2098.8 seconds.

3) Lastly, I plug the three numbers in to my equation (d = r times t) and got distance equals 390,376,800 miles, which approximately equals 390 million miles.

Ch. P - Applying Linear Equation in Two variables

For this project, I chose to do problem #8 on page 38. The problem required:

(a) Write a linear equation for Americans' income in y in terms of the year x using the points (1998, 7.4) and (1999, 7.8).

First - I used m= y2 - y1/ x2-x1 and substituted my points in to find the slope.

Second - I used slope-intercept form which is y=mx + b to find the linear equation so I can get the y-intercept.

Third - I get my equation which is y=0.4x - 791.8

(b) Use the equation in (a) to estimate Americans' income in 2001.

First - Find y when x=2001 in slope-intercept form. Put 2001 in for the x value in the equation from (a).

Second - The answer will be 8.6 trillion which is only 0.1 off from 8.7 trillion.

(c) Use the equation in (a) to predict Americans' income in 2008.

First - Use the same steps as (b), but instead of 2001, use 2008.

Second - The answer will be 10.4 trillion.

(d) Superimpose a graph of the linear equation in (a) on a scatter plot of the data.

First - I used my graphing calculator to make my scatter plot by plugging in all the points.

Second - I pressed the [Y=] button and plugged in my equation from (a).

Third - You will see a line running through the first 2 points in your scatter plot and touching the other points.

By finding the slope and using the slope-intercept form to write a linear equation, I am able to estimate and predict Americans' income for any year that I want.

Apply Linear Equation in two Variables

I'm doing Example 8 from page 38 Chapter P.4 and it asks me to find the Linear Model for Americans' Personal incomes.

On question (A) i use the point that were given (x1, y1), (x2, y2) ..(1998, 7.4), (1999, 7.8) I used the formula to find for the slope which is (y2-y1 over x2-x1) Then after i got the slope i find the y-intercept by pluging the slope and point (1998, 7.4) into the equation of the slope-intercept form. Then i got this equation (y=0.4x-791.8) in the form of (y=mx+b)

Then, on (B) i just plug (2001) in to the equation to find the income of American in the year of 2001.

On (C) , it's basically the same as (b) but in a different year. I used the year of 2007 on that one.

(D) Is where a graph is shown from 1998-2006 (The American Income)

(E) Ask me that what may have happened that from 2000-2007 that can effect the income. I said that WAR can dicrease the American Income because it causes loss of jobs as well as homeless.

Chapter P Project.

For my project, I did P.4 example 8. For the example, you need to find the slope, y2-y1/x2-x1 of the points that were given. After you find the slope, you then plug the slope into the point-slope intercept form, y-y1=m(x-x1) to make a linear equation, Ax+By=C. Then simplify the equation to a point intercept form, y=mx+b where y is by itself. And also graphing the answers I got with the equation..

Chapter P-Applying Linear Equations in Two Variables

In Chapter P, we see the usage of linear equations and graphs to solve real life problems. In this case, my project was based on Astronomy. I am suppose to use the linear equation d= r X t (distance= rate X time) to make the calculations with r= 186,000 miles/second. The planet I chose to do was Venus, so for the problem I just searched up the distance from the Moon to Venus, how fast the light travels from Venus to the Sun, and how long it takes for light to travel from the Sun to Venus. Using the information i searched up, I just plugged in the numbers to get my answer.

Chapter P: Applying Linear Equations in Two Variables

Chapter P focuses on linear equations, (in)equalities, graphs, and scientific notation. But in my case, I did my project on using scientific notation by studying the distance, time, and rate. or in other words, the speed of light of my star, Alpha Centauri.The first thing that I did to get my answers numerically is by looking up distance of my star. Then I had to convert it from light years to miles so I would be able to simplify from seconds/miles and I got 2.46896992 x 10^13 miles which equals the same as 24, 689, 699,200,000. Next, I would use the linear equation, d= r x t (distance= rate x time) and I know the rate is 186,000 miles per second. And finally, I would put my distances into the right variable in the equation and solved to find the approximation of an origin to my star.

Ch. P - Applying Linear Equation in Two variables

My project revolves around the speed of light. First, i had to search up information I needed to help solve my problems numerically such as distance and time that light traveled. Next, I had to convert kilometers into miles (1 km = 0.614 m) to make all the terms match up because the textbook gave me miles per second while the information i searched up gave me kilometers per second. Then, I used the linear equation d = r x t (distance = rate x time) to make calculations with r = 186,000 miles per second. Finally, i substituted the distances into the equations to find the time it takes light to reach an astronomical body from the origin or the place where i started from and substituted the time it takes to reach an astronomical body to find the distance between the two bodies. All calculations was solved with a calculator because the numbers were big to work with.

Ch. P - Applying Linear Equation in Two Variables

Generally speaking, option 4's chapter P project consists of the application of the distance and time of astronomical objects/bodies in the solar system by according to the speed of light. I am personally assigned to compare the distances and times that it takes for Neptune to travel to Triton (Neptune's moon), the Sun, and the Earth with the speed of light. As you know, the speed of light is approximately 186,000 miles per second. I applied this with the equation d = r x t, in which d is the distance, t is the time, and r is the rate (Distance = Rate x Time). As you will see below here, I will apply the distance formula to the space between the bodies in the solar system by solving each one algebraically and numerically.

Ch. P - Applying Linear Equation in Two Variables

Chapter P-4 is based on linear equations. Linear equations are algebraic equations of the form y = mx + b, where x and y are variables, m is the slope of the equation, and b is the constant. Linear equations intersect the y-axis at the y-intercept while the x-axis at the x-intercept. Linear equations only have one x-intercept. If we were to find an equation from a slope and two points, we use the point-slope formula, (y -y1) = m(x - x1). Then the equation will always come out to be in the form of y = mx + b.

Chapter P, Applying Linear Equations in Two Variables

Chapter P is mainly about linear equations. A linear equation can be be represented as Ax+By+C=0 and you can use this to find the x-intercept and y-intercept. Linear equations only have one point of intersection on the x-axis and these can be found in equations such as slope-intercept form or point-slope form.

Ch P, Applying linear equation to 2 variables

Ch P is mainly about linear equations. Linear equations come in different forms. There's pt- slope form, (y-y1)=m(x-x1), where you use the slope and one pt in the graph to find the equation. Another, and the most commonly used is the slope-intercept form, y=mx+b. Y equals the vertical position of a pt.(y-axis), x equals the horizontal position of a pt.(x-axis), and b is the y-intercept.

Ch. P Project - Applying Linear Equation in Two Variables

In chapter P the book talks about Linear Equations which are strait lines and only cross the y-axis and x-axis once. Whose general form is Ax+By+C=O. Which you can use to find the
y-intercept (o,y) and x-intercept (x,0). The general form of the linear equation can be transformed to different forms: slope-Intercept form-y=mx+b where m is the slope and b is the y-intercept of the equation and are constant, and point-slope form:
y - y 1 = m(x - x 1 ). You use the slope-intercept form to plug it in your graphing calculator and graph it.

In this project, I chose to find a linear model for American's personal income and find out the values in certain years. I used the slope-intercept form to write out the equation and below is my work and graph of my equation.

Ch. P - Applying Linear Equation in Two Variables

Chapter P talks about the linear equation. A linear equation can be represented by the general form Ax+By+C=0 which you can use to find the x-intercept and y-intercept. The equation can be transform into different forms, such as point-slope form or slope-intercept form, depending on what information is given and what you're trying to find. Point-slope form gives you a point and the slope and can be use to find a linear equation. While, the slope-intercept form gives you the slope and y-intercept and can be use to graph a line in a graphing calculator.

Linear Equations - Chapter P Project

Chapter P Lesson 4 focuses on linear equations. Linear equations are straight lines modeled by the equation y=mx+b, where m and b are constants. m is the slope of the equation while b is the y-intercept. Linear equations intersect the y-axis at the y-intercept and the x-axis at the x-intercept. Unlike quadratic equations, linear equations only have one x-intercept. To create an equation from a slope and two points, we use the point-slope form of a linear equation which is: y-y₁=m(x-x₁).

In this project, I chose to find the appreciation of stock value. To do this, I will use linear equations to estimate how stock value increases over time.