Standard FormStandard FormAx + By = CAx + By = C

SlopeSlope y-intercepty-intercept x-interceptx-intercept

3x – 4y = 243x – 4y = 24

––1/21/2 3 3

2x – 5y = –102x – 5y = –10

nonenone – – 77

3/43/4 – – 66 88

x + 2y = 6x + 2y = 6 66

2/52/5 22 – – 55

x = – 7 x = – 7 undefinedundefined

y – y1 = m (x – x1)m = slope

x1 = x-coordinate of point on liney1 = y-coordinate of point on line

To convert to Slope-intercept Form: Distribute the slope. Move y1 to right side of the equal sign.

ExampleExample 05/04/2305/04/23

Give an equation in Standard Formfor the line that has a slope of passes through the point (8, –2). Find the x-int and y-int.

)( 11 xxmyy Slope = – 2 and (8, –2) ))8()(

23()2( xy

12232 xy

Point-Slope Form →

Substitute your given values →

Distribute →

)8(232 xy

23

Continue →

Continued Continued 05/04/2305/04/23

Multiply by – 2 →

Standard Form →

Continued from the previous slide →

1423

yxPut into Standard Form →

1423

xySolve for y →

12232 xy

]1423[2 yx

2823 yxx-int = 28/3y-int = –14

ExampleExample 05/04/2305/04/23

Give an equation in Standard Formfor the line that passes through thepoints (3, 5) and (6, – 1)

3651slope

)( 11 xxmyy Slope = – 2 Pick one of the given points. Let’s pick (3, 5)

))3()(2()5( xy

625 xy112 xy112 yx

Point-Slope Form →Substitute your given values →

Distribute →Solve for y →

Put into Standard Form →

)3(25 xy

Example ContinuedExample Continued 05/04/2305/04/23

Give an equation in Standard Formfor the line that passes through thepoints (3, 5) and (6, – 1)

3651slope

)( 11 xxmyy Slope = – 2 Pick one of the given points. Let’s pick (6, –1)

))6()(2()1( xy

1221 xy112 xy112 yx

Point-Slope Form →Substitute your given values →

Distribute →Solve for y →

Put into Standard Form →

)6(21 xy

Example Example 05/04/2305/04/23

Give an equation in Standard Formfor the line that has an x-int 3 and y-int 7.

3007slope

)( 11 xxmyy

Slope = – 7/3 Pick one of the given points. Let’s pick (3, 0)

))3()(37()0( xy

737

xy

737

yx

Point-Slope Form →Substitute your given values →

Distribute →

Put into Standard Form →

)3(37

xy

The ordered pairs are (3, 0) and (0, 7).

Continued→

Continued Continued 05/04/2305/04/23

]737[3 yxMultiply by 3 →

2137 yxStandard Form →

737

yxContinued from the previous slide →

Example Example 05/04/2305/04/23

Last week, Mr. Baxter sold $20,000 worth of newspaper advertisements and earned $800. The week before, he sold $26,000 worth of advertisements and earned $860. Assume the relationship between Mr. Baxter’s weekly earnings and the value of the advertisements he sells is linear.

a)Write the data above as two ordered pairs in the form (s, e).

b) Find the slope of the line given these ordered pairs.

c) Write an equation for the line in slope-intercept form given the data.

(20,000, 800) and (26,000, 860)

Slope = .01

Continued→

Example Example 05/04/2305/04/23

Last week, Mr. Baxter sold $20,000 worth of newspaper advertisements and earned $800. The week before, he sold $26,000 worth of advertisements and earned $860. Assume the relationship between Mr. Baxter’s weekly earnings and the value of the advertisements he sells is linear. Ordered Pairs (20,000, 800) and (26,000, 860)Slope = .01c) Write an equation for the line in slope-intercept form given the data.

Slope = .01 and (20,000, 800) )( 11 xxmyy )20000(01.800 xy

20001.800 xy60001. xy

You cannot find 1 equation for a piecewise function.

You can find an equation for each part. Use the endpoints of each part to find

the slope of that segment. Use the slope and one of the points to

write an equation in point-slope form. Convert to slope intercept form. Write an inequality to define that

piece.

Use the endpoints of each part to find slope.

Write an equation in point-slope form.

Convert to slope- intercept form.

Write an inequality.

30103

)1(33 xy

103

xxy

Use the endpoints of each part to find slope.

Write an equation in point-slope form.

Convert to slope- intercept form.

Write an inequality.

41

1534

)5(414 xy

51411

41

x

xy

Use the endpoints of each part to find slope

write an equation in point-slope form

Convert to slope intercept

Write an inequality

45640

)6(40 xy

65244

xxy

30;3 xxy

51;411

41

xxy

65;244 xxy

Lesson Master 3-5. Pages 165-166 #’s 2, 5, 7-9, 13, 14, 16.

Quiz on Sections 3-4 and 3-5 on Tuesday, November 25th!!!