# Math 101 Review Sheet for Exam #2

## 3 All about lines

**3.1 The Rectangular Coordinate System**

Know how to plot points in the rectangular coordinate
system.

Know the definitions of x and y intercepts for a line. In particular,

know that these are actually points, and so you need to have two

values . For example, the x-intercept of the line described by

5x − 2y = 10

is the point (2, 0); the y-intercept for the same line is
the point

(0,−5).

Given an equation for a line, know how to plot it. In
addition

to ‘normal’ lines, you should be able to handle plotting vertical and

horizontal lines.

Try problems 35, 39, 41, 45, 47 and 49, or any additional
problems

from out of 33-50 if you feel the need.

**3.2 The Slope of a Line**

Know the definition of slope, and what geometric
significance it

carries with it. Given two points on a line, or given an equation of

a line, you should be able to compute its slope. You should know

what a slope of 0 and undefined slope means.

For example, any of 29-37 should be trivial to find the
slope of

the line.

Given a point on a line, and the slope of a line, you
should be

able to sketch a graph of the line . The point tells you where to

start, and the slope tells you how to find another point on the line.

(Think rise/run).

If you need it, try 38, 41, 42, 43, 44, 45 for practice.

Given two lines, you should be able to determine if they
are

parallel, perpendicular or neither. Questions to think about are 1.)

How do you find the slope of a parallel line? 2.) Given a line, how

do you find the slope of a perpendicular line?

Problems that ask you about these ideas are 49-60 any.

**3.3 Linear Equations in Two Variables**

This looks like the heart of the chapter. Given two pieces
of information

about a line, you should be able to write down an equation

for that line. For example, given two points on the line, or one point

on the line and the slope of the line, you should be able to write

down an equation for the line.

Oftentimes the most useful way to get an equation out of a
couple

pieces of information from a line is to use Point-Slope form:

y − y_{1} = m(x − x_{1})

where (x_{1}, y_{1}) is any point on the line, and m is the
slope of the line.

Try problems 19, 23-38 any, 41, 43, 49-60 any, 61, 65.

**3.4 Linear Inequalities in Two Variables **

Know the three step process for graphing an inequality. 1)
graph

the boundary line. (dashed if <, solid if the inequality is ≤. 2)

Choose a test point. 3) Shade the appropriate region. When you

write these problems up, be sure that the reader can follow your

work. For example, it is extremely useful to write the words ‘Use

the Test Point (0,0).’

Look at problems 7-18 any.

## 4 What Can We Do with Two Lines?

**4.1 Two Lines and their intersections**

Given two lines, we’d like to look at what happens when we
try

to ‘solve’ both of them simultaneously . Geometrically what this

means is we’d like to find any and all points the two lines have

in common . Algebraically, this means we’ d like to find all ordered

pair of numbers, (x, y) such that (x, y) is a solution to the algebraic

equation.

Look at the chart on page 226, because it helps to
understand the

geometric significance of what happens with you run into what are

called the ‘degenerate’ cases. These are the two oddball cases where

the lines happen to be parallel. If this is the case, they are either

the same line, or they never intersect. Algebraically sometimes this

isn’t obvious!

We have two ways to solve for a system of linear
equations. The

first is called elimination, and the second is called substitution . My

guess is that the exam problem testing on this won’t tell you which

method to use , so it’s up to you to pick which method is easier for

the situation.

Good problems to look at are 17-32 any and 39-54 any. Make

sure you do enough of these until you run into at least on or both

of the degenerate cases (parallel lines).

**4.2 Planes**

We skipped this section

**4.3 ‘Applications’ of Systems of Linear Equations**

The exam problem won’t be as nice as the book is. I mean
that

the exam won’t have a table set up for you to fill in. So, in order

to figure out what table to use, we try and mimic some formula we

know , such as d = rt, or amt acid = concentration x volume.

Look at problems 19, 27, 31 and 35.

Prev | Next |