MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C90D13.82D38610" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C90D13.82D38610 Content-Location: file:///C:/AAFB9E43/M117Lesson4.2-4.4doc.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Lesson 4

Lesson 4.2-4.4F’08

 

Objectives:      To determine whether a given ordered pair

            =             is a solution to a given equation.

Find solutions for an equation with two

unknowns.

To graph linear equations.

Find the coordinates of the x-and y-<= /span>

intercepts, and use them to graph a linear =

equation.

To compare lines with different slopes.

To graph equations in slope-intercept form.=

To find the slope of a line given two points

on the line.

 

EXAMPLE:  Determine whether the ordered pair= (3, 2) is

            =           a solution= for the equation y =3D 3x - 8.

 

 

 

 

 

 

 

Is ( 0, -8)?&nbs= p;            &= nbsp; 

 

 

 

 

 

 

Example:  Find three solutions for the equat= ion 2x + y =3D 12.

            =     Then use your point to graph the line.

x

y

 

 

 

 

 

 

3D"[image]"

 

 

EXAMPLE: Graph 4x - y= =3D 8.

 

Let’s first sol= ve for y,

Then find three point= s that lie on the line.

Finally graph those p= oints and connect them with a line.

 

x

y

 

 

 

 

 

 

 

3D"[image]"

 

 

EXAMPLE:  Graph            1.  x =3D -2           &nb= sp; 2.  y =3D 4

 

3D"[image]"                =             &nb= sp;  3D"[image]"

Where do the lines cr= oss the axis?

 

What are the coordina= tes of the x and y intercept for the following graph?  The point where a graph intersects to x-axis is called the x-intercept.<= span style=3D'mso-spacerun:yes'>  The point where the graph intersec= ts the y- axis is called the y intercept.

3D"[image]"

To find the x and y intercepts from an equation:

To find the x-interce= pt:        &= nbsp;           &nbs= p;        To find the x-intercept:

1.  Replace y with 0 in the         &= nbsp;           &nbs= p;  1.  Replace x with 0 in the

     given equation.<= span style=3D'mso-tab-count:4'>        &= nbsp;           &nbs= p;            &= nbsp;         given equa= tion.

2.  Solve for x.            =             &nb= sp;            =       2.  Solve for y.

 

EXAMPLE:  Find the x and y intercepts for ea= ch equation.

        1.  2x + 6 y =3D 18     2.  y =3D 3x + 1(note the significances of the 1)

EXAMPLE:  Graph each of the following on the= same grid.

 

 

1.  y =3D x blue       2.  y =3D 2x red      3.  y =3D <= ![endif]>xgreen    4.  y =3D -2xlime

3D"[image]"

 

How does the coeffici= ent of x affect the graph?  =

This coefficient is c= alled the slope.

 

In the equation y =3D= mx + b, m is the slope and (0,b) is the y-intercept.

 

 

 

SLOPE-The ratio of the vertical change between any two

        points on a line to the horizontal change between these

two points.

Find the slope of the= line containing the points:  (4, -2) and (6, 4)

3D"[image]"

The Slope Formula

Given two points(x1, y1) and (x2, y2), where x2<= ![endif]>x1, = the slope of the line containing the two points is given by the formula

  m =3D <= ![endif]>.

 

 

 

 

EXAMPLE:  Find the slope of a line containin= g the points(2, -4) and ( -4, 6)

 

 

 

 

 

EXAMPLE:  Graph y =3D -<= ![endif]>x + 2<= /p>

3D"[image]"

Class work Worksheet 4.2-4,4

Homework Math XL sections 4.2-4.44

 

DUE BY_____________________

 

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