Lines, Lines, Lines!!!Lines, Lines, Lines!!!~~

Standard FormStandard Form

Another equation of the Another equation of the same line.same line.

What we Have Learned What we Have Learned so far….so far….

Slope Intercept Form

bmxy

Where m is the slope and b is the intercept

What we Have Learned What we Have Learned so far….so far….

Point-Slope Form

11 xxmyy

Where m is the slope and are a point on the line. 11,yx

We will use our prior knowledge of We will use our prior knowledge of

Slope-Intercept FormSlope-Intercept Form

&&

Point-Slope FormPoint-Slope Form

To learn about the To learn about the Standard FormStandard Form of a of a Line:Line:

Ax + By = CAx + By = C

Standard Form Standard Form

The Standard Form of a Linear Equation isThe Standard Form of a Linear Equation is

Ax + By = CAx + By = C

Where A Where A ≥ 0, ≥ 0, &&A and B are not both zeroA and B are not both zero&&A, B, and C are integers whose greater A, B, and C are integers whose greater

common factor is 1. common factor is 1.

Standard Form Standard Form

The Standard Form of a Linear Equation isThe Standard Form of a Linear Equation is

Ax + By = CAx + By = C

Notice that: x and y have exponents of 1 x and y are not multiplied together x and y do not appear in

denominators, exponents, or radicals

Examples of Standard FormExamples of Standard Form

These Equations These Equations are in Standard are in Standard Form:Form:

2x + 5y = 72x + 5y = 7

x – y = - 10 x – y = - 10

1000x + 75y = 61000x + 75y = 6

These Equations are These Equations are not not in Standard in Standard Form:Form:

1/2x + 2/3y = 61/2x + 2/3y = 6

12x – 36y = 10

5ix + 7py = -29

Question:Question: Is the equation 4x + 7y = -10 a

linear equation? Explain why.

This equation is a linear equation because it is in standard form with A = 4, B = 7, and C = –10.

Is the equation 2xy = 4 a linear equation? Explain why.

This equation is not a linear equation because x and y are multiplied by each other.

Writing an equation in Standard Form Writing an equation in Standard Form Ax + By = CAx + By = C

y = 2/5x - 3y = 2/5x - 3

(5)(5)y = (2/5x - 3)y = (2/5x - 3)55 5y = 2x - 155y = 2x - 15 5y 5y -2x-2x = 2x = 2x -2x-2x – 1 – 1 -2x + 5y = -15-2x + 5y = -15 -1(-2x + 5y = -15)-1(-2x + 5y = -15) 2x – 5y = 152x – 5y = 15A= 2, B= -5, and C = 15A= 2, B= -5, and C = 15

Writing an equation in Standard Form Writing an equation in Standard Form Ax + By = C Ax + By = C

Given A Point and a SlopeGiven A Point and a Slope Point (3,4) and m = 6Point (3,4) and m = 6 y - y1 = m(x - x1) y - y1 = m(x - x1) Use Point-Slope Form Use Point-Slope Form y - 4 = 6(x - 3) y - 4 = 6(x - 3) Substitute the values Substitute the values y - 4 = 6x – 18 y - 4 = 6x – 18 Use Distributive Property Use Distributive Propertyy - 4 + 4 = 6x - 18 + 4 y - 4 + 4 = 6x - 18 + 4 Add Liked Terms Add Liked Terms y = 6x – 14 y = 6x – 14 Slope-Intercept Form Slope-Intercept Form -6x + y = 6x – 6x – 14 -6x + y = 6x – 6x – 14 Move the x value Move the x value -6x + y = -14 -6x + y = -14 Add Liked Terms Add Liked Terms-1(-6x + y = -14) -1(-6x + y = -14) Multiply times -1 Multiply times -16x – y = 14 6x – y = 14 Standard Form Standard Form

Writing an equation in Standard Form Writing an equation in Standard Form Ax + By = C Ax + By = C

Given Two Points (6, -2) and (-4, 4)Given Two Points (6, -2) and (-4, 4)

First: Find the Slope between the two points

Second: Use the Slope and the first point on the Point-Slope Form. Plug them in.

Writing an equation in Standard Form Writing an equation in Standard Form Ax + By = C Ax + By = C

Given Two Points (6, -2) and (-4, 4)Given Two Points (6, -2) and (-4, 4)

A = 3, B = 5 and C = 28

Graph 2 x + 3 y = 12

1.Already using standard form: 2 x + 3y = 12

2. Let y = 0 2 x + 3(0) = 122 x = 12 x = 6 x-intercept is at ( 6 , 0 )

3. Let x = 0 2 (0) + 3 y = 12 3 y = 12 y = 4

y-intercept is at ( 0 , 4 )

Steps to Graph Equations in standard formSteps to Graph Equations in standard form1.Write the equation in standard form2.Find x-intercept, by letting y = 0, solve for x, plot the point where x crosses the x-axis3.Find y-intercept, by letting x = 0, solve for y, plot the point where y crosses the y-axis4.Draw a line through the 2 points.

( 0 , 4 )

( 6 , 0 )

•

•

2 x + 3 y = 12

Your Turn!Your Turn!How do you graph a line which is in How do you graph a line which is in

standard form?standard form?Graph 3x - 4y = -12

x y0 (3)0 - 4y = -123

0 3x - (4)0 = -12-4

Graph the points and connect the dots

-5 5

4

2

-2

-4

Student ActivityStudent ActivityYou will now receive a You will now receive a worksheet. Turn the worksheet. Turn the worksheet in when worksheet in when

completed.completed.

Do Not DisturbDo Not DisturbWork In ProgressWork In Progress