Algebra 2 Test Research Guide

Can H. and Blaine H.

The Intercept Method:

-The x-intercept of a line is the point where a line passes across the x-axis. Its heads are (#, 0). -The y-intercept of the line is the point in which a line passes across the y-axis. Its coordinates are (0, #). 1- Find the x-intercept by simply letting y=0.

2- Locate the y-intercept by permitting x=0.

3- Plot the intercepts and graph the line. (If the x and y intercepts are both 0, use a desk to find the second point. )

Ex:

x-int:

5x-3y=-30

y=0

5x-3(0)=-30

5x=-30

вЂ“вЂ“ вЂ“вЂ“

5

your five

x= -6 (-6, 0)

y-int:

x=0

5(0)-3y=-30

вЂ“вЂ“ вЂ“вЂ“

-3 -3

y=10 (0, 10)

The Slope-Intercept Method:

- The Slope-Intercept form of a line is usually y=mx+b, where b is a y-intercept ( a point ) and m is the slope.

- Incline is a zone of two numbers.

в€†=" deltaвЂќ(change)

Incline Definition:

m= Rise

вЂ“вЂ“вЂ“вЂ“

Run

в€†y

y a couple of - y1

вЂ“вЂ“вЂ“ sama dengan вЂ“вЂ“вЂ“вЂ“вЂ“вЂ“вЂ“

в€†x

x 2 - x1

1- Resolve for sumado a to put the equation in slope intercept form.

2- Plot the y-intercept.

3- Using the slope as a fraction, rise sumado a and manage x to get second point. 4- Graph the line.

Ex:

2x+3y=12

-2x

-2x

вЂ“вЂ“вЂ“вЂ“вЂ“вЂ“вЂ“вЂ“вЂ“

3y=-2x+12

вЂ“вЂ“ вЂ“вЂ“вЂ“вЂ“

3

3

y= -2/3x+4

m= -2/3 b= 4

Horizontal and Vertical Lines:

- A Horizontal Range has the contact form y=#. (In an equation of a horizontally line, you cannot find any x) -- The slope of a side to side line is definitely 0. Photo:

(can walk on the line)

- A Vertical Series has the contact form x=#. (In an equation of a vertical line, you cannot find any y. ) - The slope of a vertical range is undefined. Picture:

(falls off line)

- (*y-intercept = non-e parallel to y-axis until x=0)

1- If con is the just variable, solve for y.

2- Attract a horizontal line that crosses the y-axis in what sumado a equals. OR PERHAPS

1- If perhaps x is definitely the only varying, solve intended for x.

2- Draw a vertical range that crosses the x-axis at what x equals. Ex:

Graph y=-3 and 2x-1=3

(Horizontal ^)

plus one +1

2x=4

вЂ“вЂ“ вЂ“вЂ“

2 two

x=2

(Vertical ^)

Extra:

Point Incline Formula: y-y1=m(x-x1)

Standard Formulation: Ax+By=C

Equations of Thready Functions from other Graphs (3. 4)

Assessment formulas from 3. 1-3. 3

Slope Intercept type is y=mx+b where " mвЂќ signifies the incline and " bвЂќ presents the yintercept вЂў y-intercept - an event is the worth of y when x=0

вЂў x-intercept - an event is a benefit of back button when y=0

Slop formulation is surge over work, where

y = # is a graph of a side to side line with a slope comparable to 0

by = # is a chart of a top to bottom line using a slope corresponding to undefined

Level slope contact form is con вЂ” y1 = m(x вЂ” x1), where " mвЂќ represents the incline and вЂ”y1, вЂ”x1 represents the point

Normal form can be Ax & Bx = C

Suppose someone says, " In the event the equation is definitely y = 3x вЂ” 8, precisely what are the slope and y-intercept? Slope is definitely 3 and y-intercept is definitely вЂ”8

In the event the slope and y-intercept are вЂ”5 and 13, what is the formula? y sama dengan вЂ”5x+13 With this section you are going to use information about the graph to publish equations of particular lining functions

Aim: Given the data about the graph of your liner function write it is particular formula

Example you: Find the particular equation with the linear function with the slope вЂ”3/2, made up of the point (7, вЂ”5)

Because the point and slope get the easiest kind to use is a point slope form. You would write: con + five = вЂ”3/2(xвЂ”7)

Example 2: Find the particular equation with the linear function containing the points (вЂ”4/5) and (6, 10)

Initial using the slope formula to find the slope, meters

10 вЂ” 5

вЂ”5

m = вЂ”вЂ”вЂ”вЂ”вЂ”вЂ” = вЂ”вЂ”вЂ”вЂ” sama dengan 0. a few

6+4

12

You can use either of the given points inside the point slope form yвЂ”5 = zero. 5(x+4) or perhaps yвЂ”10 sama dengan 0. 5(xвЂ”6)

Distribute and simplify both equally equations over into slope intercept kind y вЂ” 5 = 0. 5x + a couple of

y вЂ” 10 = 0. 5x вЂ” 3

y= zero. 5x & 7

or perhaps y = 0. 5x + 7

Two lines are seite an seite to each other in case their slopes are equal. Two lines will be perpendicular to each other the incline of one is definitely the opposite of the reciprocal of the other

Parallel and Perpendicular Lines

If the formula of a range is sumado a = mx + b, then: вЂЁ

A seite an seite line has slope " mвЂќ

A perpendicular line has a incline вЂ”1/m...