College Algebra K/DCFriday, 23 January 2015

• OBJECTIVE TSW write equations for lines in standard form and slope-intercept form.

• ASSIGNMENT DUE I will take a few HW questions before turning it in.

– Sec. 2.4: pp. 227-231 (65-68 all, 73-77 all, 88-92 all) wire basket

R2-2

Equations of Lines; Curve Fitting2.5Standard Form ▪ Slope-Intercept Form ▪ Point-Slope Form

Equations of Lines

Standard FormAx + By = CA, B, and C are integersA is positive

Slope-intercept Formy = mx + bm is the slope, b is the y-intercept

Point-Slope Form

y – y1 = m(x – x1)

m is the slope, (x1, y1) is any point on the line

2-4

Find an equation of the line through (3, –5) having slope –2. Write the answer in slope-intercept form.

Using the Point-Slope Form (Given a Point and the Slope)

Point-slope form: y – y1 = m(x – x1)

x1 = 3, y1 = –5, m = –2

2 1y x

2-5

Find an equation of the line through (–4, 3) and (5, –1). Write the answer in slope-intercept form.

Using the Point-Slope Form (Given a Point and the Slope)

First, find the slope:

Use either point for (x1, y1)

Point-slope form

4 11

9 9y x

2-6

Find the slope and y-intercept of the line with equation 3x – 4y = 12.

Find the Slope and y-intercept From an Equation of a Line

Write the equation in slope-intercept form:

The slope is and the y-intercept is –3.

Also, m = −A/B, b = C/B.

2-7

Find an equation of the line through (–2, 4) and (2, 2). Then graph the line using the slope-intercept form.

Using the Slope-Intercept Form (Given Two Points)

First, find the slope:

The equation is

Substitute for m and the coordinates of one of the

points (say, (2, 2)) for x and y into the slope-intercept

form y = mx + b, then solve for b:

2-8

Using the Slope-Intercept Form (Given Two Points)

2-9

Use the graph to (a) find the slope, y-intercept, and x-intercept, and (b) write the equation of the function.

Finding an Equation From a Graph

The line rises 5 units each time the x-value increases by 2 units.

The slope is .

2-10

Finding an Equation From a Graph

The graph intersects the y-axis at (0, 5) and the x-axis at (–2, 0).

The y-intercept is (0, 5).

The x-intercept is (–2, 0).

2-11

Finding an Equation From a Graph

Slope , y-intercept 5

Converting to Standard Form

Convert the following to standard form.

15

2f x x

Ax By C A, B, and C are integers,

A is positive.

15

2y x

2 10y x

2 10x y

2 10x y

Converting to Standard Form

Convert the following to standard form.

133

4f x x

Ax By C

133

4y x

4 12 13y x

12 4 13x y

Converting to Standard Form

Convert the following to standard form.3 1

5 2y x

10 6 5y x

6 10 5x y

6 10 5x y

The LCD is 10, so multiply both sides by 10.

3 1

20

51 10y x

1-4) matching equations with graphs (get from the book on your own)

Write an equation for the line described. Give answers in standard form (Ax + By = C).

5) through (1, 3), m = –2 6) through (2, 4), m = –1

7) through (–5, 4), 8) through (–4, 3), m = –3/2 m = 3/4

Write an equation for the line described. Give answers in slope-intercept form (y = mx + b).

13) through (–1, 3) & (3, 4) 14) through (8, –1) & (4, 3)

15) x-int. 3, y-int. –216) x-int. –2, y-int. 4

21) m = 5, b = 15 22) m = –2, b = 12

23) m = –2/3, b = –4/5 24) m = –5/8, b = –1/3

Give the slope and y-intercept and graph.

31) y = 3x – 1 32) y = –2x + 7 33) 4x – y = 7

34) 2x + 3y = 16 35) 4y = –3x 36) 2y – x = 0

37) x + 2y = –4 38) x + 3y = –9 39) y – 3/2x – 1 = 0

Sec. 2.5: p. 242 (1-8 all, 13-16 all, 21-24 all, 31-39 all) Due on Monday, 26 January 2015.

College Algebra K/DCMonday, 26 January 2015

• OBJECTIVE TSW write equations for lines in standard form and slope-intercept form.

• ASSIGNMENT DUE– Sec. 2.5: pp 242-243 (1-8 all, 13-16 all, 21-24 all, 31-

39 all) wire basket

• QUIZ: Sec. 2.4 & 2.5 is tomorrow, Tuesday.

• Get out your complimentary straightedge.

• IN-CLASS ASSIGNMENT– ACTIVITY: Parallel and Perpendicular Lines– When you finish, work on today’s assignment

(due tomorrow).

R-17

Equations of Lines; Curve Fitting2.5Vertical and Horizontal Lines ▪ Parallel and Perpendicular Lines

Vertical and Horizontal Lines

Vertical lines– Have undefined slopes– Are of the form x = a (a is a constant)– Have No y-intercept (except when the line is x = 0)– Are not functions

Horizontal lines– Have slopes equal to 0– Are of the form y = a (or f (x) = a) (a is a constant)– Have no x-intercept (except when the line is y = 0)– Are constant functions.

In-Class Activity: Parallel and Perpendicular Lines• You may work with someone.• Due before you leave today (black

tray).

Assignment – Sec. 2.5: pp. 242-244 (9-12 all, 17-20 all, 25, 26, 28, 47-56 all) Due on Tuesday, 27 January 2015.Write an equation for the line described. Give answers in standard form (Ax + By = C).

9) through (–8, 4), m undefined

10) through (5, 1), m undefined

Write an equation for the line described. Give answers in slope-intercept form (y = mx + b).

11) through (5, –8) m = 0 12) through (–3, 12) m = 0

17) vertical through (–6, 4) 18) vertical through (2, 7)

19) horizontal through (–7, 4) 20) horizontal through (–8, –2)

25) slope 0, y-int 3/2 26) slope 0, y-int –5/4 28) matching – get from bookWrite an equation (a) in standard form and (b) in slope-intercept form for the line described.

47) through (–1, 4), parallel to x + 3y = 5

48) through (3, –2), parallel to 2x – y = 5

49) through (1, 6), perpendicular to 3x + 5y = 1

50) through (–2, 0), perpendicular to 8x – 3y = 7

Assignment – Sec. 2.5: pp. 242-244 (9-12 all, 17-20 all, 25, 26, 28, 47-56 all) Due on Tuesday, 27 January 2015.Write an equation (a) in standard form and (b) in slope-intercept form for the line described.

51) through (4, 1), parallel to y = –5

52) through (–2, –2), parallel to y = 3

53) through (–5, 6), perpendicular to x = –2

54) through (4, –4), perpendicular to x = 4

55) Get from the book. Be sure you can do this.

56) Get from the book. Be sure you can do this.