D.U. writes:
Chapter 3 challenged the students' skills in using everyday problems and translating them into graphs, respectively the use of graphs in everyday problems such as figuring out terms in sequences whether they be in explicit or recursive forms. Scatterplot and step graphs were also used to portray problems dealing with statistics and other forms of random data. We were also taught that standard equations forms can be used to portray direct variation problems. From here we can accurately portray the slope and different values for the graph dealing with the data. Therefore, in closing, chapter 3 taught advanced algebra students how to portray everyday problems using different types of graphs.

S.C. writes:
We studied constant increase and decrease situations. We studied the graph of y=mx+b and the linear-combination situations. We also studied the graph of ax+by=c and how to find an equation of a line. We studied how to fit a line to data and how to use Recursive formulas for arithmetic sequences. And last but not least we learned step functions.

A.K. writes:
Chapter 3 was about graphing functions and data useing equations. We used y=mx+b and ax+by=c equations. We learned how to calculate slope and the x and y intersepts of a line. We also learned what to call the different kinds of graphs.

Chapter 3 was about graphing functions and data useing equations. We used y=mx+b and ax+by=c equations. We learned how to calculate slope and the x and y intersepts of a line. We also learned what to call the different kinds of graphs.

K.W. writes:
1. Chapter 3 was about linear functions. The book reviewed situations in which constant increase or decrease occured. We also used different equations to describe lines, such as y=mx+b, ax+by=c, and y-y1=m(x-x1). Scatterplots and fitting lines to data, as well as linear combinations and explicit formulas, recursive formulas, and step functions, were all reviewed in this chapter.
2.

N.G. writes:
Chapter three was called Linear Functions. We learned all about linear functions: how to solve and graph them. In the first lesson, we learned about constant increase and decrease. In lessons two, four and five we learned about slope and the equations of lines. In lesson 6, we leanred to graph this data and fit a line to a scatterplot. Lesson three was about combining linear data and graphing it. In lessons seven and eight, we applied things learned in previous chapters: recursive and explicit formulas. Finally, in the last lesson, we learned about step functions and how to solve and graph them.

A.M. writes: 1. Chapter three dealt with linear functions. The chapter began with constant-increase and constant-decrease situations. It continued by talking about the graph of the line y=mx+b. Next, we learned about linear-combination situations. In the following section, we were taught a new form of writing the equation of a line, Ax+By=C. This form is known as standard form equation of a line. Continuing on, finding the equation of a line when given two points was the highlight of the next section. Another form of writing the equation of a line was also shown. The point-slope equation, which is (y-y1)=m(x-x1). Making progress, we learned about fitting a line into data. In the next couple of sections, learned about recursive and explicit formula for arithmetic sequences. Lastly, we learned about step functions. Chapter three was a very interesting chapter. 2. Chapter three dealt with linear functions. The chapter began with constant-increase and constant-decrease situations. It continued by talking about the graph of the line y=mx+b. Next, we learned about linear-combination situations. In the following section, we were taught a new form of writing the equation of a line, Ax+By=C. This form is known as standard form equation of a line. Continuing on, finding the equation of a line when given two points was the highlight of the next section. Another form of writing the equation of a line was also shown. The point-slope equation, which is (y-y1)=m(x-x1). Making progress, we learned about fitting a line into data. In the next couple of sections, learned about recursive and explicit frormula for arithmetic sequences. Lasstly, we learned about step functions. Chapter three was a very interesting chapter.

E.W. writes:
1. We learned many new and interesting things in chapter 3. First off, we learned about constant increase and constant decrease situations. Then we began to learn differnet equations. WE started with the graph of y=mx+b. Then we learned linear-combination situations. Then we learned the gr5aph of Ax+By=C equation. Then we learned how to find an equation of a line.Then we learned how to take a line and fit it into data. Then came recursive formulas for arithmetic sequences, i though that this was rather easy. Explicit formulas, which we learned next was even easier. After that we learned step functions which also were pretty easy. Overall io thought that this lesson was kind of easy.

2. In Chapter 3 we learned linear functions. There were three main equations that we used. the Standard Equation -- Ax+By=c Slope Intercept y=mx+b. Point slope equation y-y1=m(x-x1) We also learned how to graph these equations, using constant increase and constant decrease. Linear combinations were also discussed where we use monkey roll, to solve these questions. We later learned how to fit a line to data by plugging in numbers using linear regression. Explicit and recursive formulas were also used to show constant increase or constant decrease. In the last section, step equations were used. Using X, the greatest integer less than or equal to, we can graph points like steps.

M.B. writes:
Chapter three was very interesting and full of new concepts. We learned about linear functions with point-slope, linear combinations, constant increases or decreases, and step functions.We learned that the y intercept is the initial condition or the starting point in a situation. I know understand the idea of a graph that is called a piecewise linear. We learned about slope (same slope makes parallel lines and the inverse). We learned how to use and create linear combinations and how to determine their domain. We learned the standard form of an equation for a line is Ax+By=C and what each stands for. In the slope intercept we learned that m is the slope and b is the y intercept. Using the monkey rule we çan also figure out what the x intercept is. We learned how to use the point-slope equation, or y-y1=m(x-x1). NOW WE HAVE SEVERAL WAYS TO GIVE THE EQUATION FOR A GRAPH. We learned how to program numbers into our calculators to make a scatterplot and then make a regression line (the line that is the best fit or the least squares line). The correlation coefficient is a number from negative one to one that indicates if the slope is positive or negative and the ab. value of r gijves the strength of the linear relationship. We also used our previous knowledge of recursive and explicit formulas to make arithmatic sequences using explict and regressive formulas. We then learned step functions with the greatest integer symbol and function (rounding down function or the floor function).

M.B. writes:
IT WAS INTERESTING TO LEARN VARIOUS WAYS TO SLOPES (CONSTANT INCREASE OR DECREASE), Y-INTERCEPTS, AND X-INTERCEPTS. (IE: STANDARD EQUATIONS AX+BY=C, SLOPE-INTERCEPTS EQUATIONS Y=MX+B, ETC.) WE ALSO COVERED THE RECURSIVE AND EXPLICIT FORMULAS IN FURTHER DETAIL THAN WERE COVERED IN CHAPER 1-7 AND 1-8, AS THEY RELATE TO ARITHMETIC SEQUENCES. STEP FUNCTIONS WERE ALSO INTRODUCED. ON A WHOLE, THE CHAPTER WAS FAIRLY EASY, BECAUSE IT WAS NOT THE FIRST TIME I HAD BEEN INTORDUCED TO THE MATERIAL.HOWEVER, IT SERVED AS A GOOD REVIEW.

C.A. writes:
In chapter three we learned about three different equations. The three equations were standard Ax+By=C, point-slope y-y1=m(x-x1), and the last was slope-intercept y=mx+b. It was hard to understand how to change each equation into another. I learned about step function and we did explicit formula and recursive formulas again so that my understanding became clearer.Making scatter plots and fitting a line to it, and also how to make a scatter plot on a graphing calulator. And I also learned about constant increase and constant decrease. I also learned what a step function and a liner combination is. Over all the chapter was difficult but after a while I got a better understanding of the over all material.

C.A. writes:
IN CHAPTER 3 WE LEARNED LINEAR EQUATIONS. WE USED 3 DIFFERENT EQUATIONS. ONE WAS IN THE FORM OF AX+BY=C. THAT IS ALSO CALLED THE STANDARD FORM. THE SLOPE INTERCEPT FORM IS WRITTEN Y=MX+B, WHERE M IS THE SLOPE AND B IS THE Y INTERCEPT. THE THIRD KIND OF EQUATION THAT WE STUDIED IS CALLED POINT SLOPE, AND IT IS SHOWN BY Y-Y1=M(X-X1). IN THIS EQUATION THE VARIABLE M IS THE SLOPE. WE ALSO LEARNED THAT HORIZONTAL LINES HAVE NO SLOPE, AND VERTICLE LINES HAVE AN UNDEFINED SLOPE. OBLIQUE LINES CAN EITHER HAVE A POSITIVE SLOPE OR A NEGATIVE SLOPE. IN THIS CHAPTER WE ALSO DID A REVIEW OF RECURSIVE AND EXPLICIT FORMULAS. OTHER GRAPHS WE DID ARE STEP GRAPHS, WHICH LOOK LIKE STEPS OF A STAIRCASE BECASUE IT GRPAHS SOMETHING WITH LESS THAN OR GREATER THAN EQUATIONS.