College Algebra K/DCMonday, 27 January 2014

• 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

• Everything is pushed back one day.

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

Assignment

• Sec. 2.5: p. 242 (1-8 all, 13-16 all, 21-24 all, 31-39 all)– Due Tuesday, 28 January 2014.

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 Tuesday, 28 January 2014.

College Algebra K/DCTuesday, 28 January 2014

• 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)

• QUIZ tomorrow (sec. 2.4 & 2.5).

• Please pick up a straight edge from the front.

Parallel and Perpendicular Lines

Today’s activity is for a grade. You will need

graph paper, a straightedge, and a pencil.

R-19

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.

Parallel and Perpendicular Lines1) On your graph paper, graph the line 4x – 3y = 9.

What is the slope? (write it on your graph)

2) On the same graph, graph the point (–1, 2) and draw a line parallel to the first line through that point.

3) Write the equation (in standard form) for this new line. (Use the point-slope form y – y1 = m(x – x1).)

What is the equation (standard form)?4x – 3y = –10

4) Write the equation (in slope-intercept form) for this new line.What is the equation (slope-intercept form)?

Parallel and Perpendicular Lines5) On another graph, graph the same line (4x – 3y = 9)

and write the slope on your graph paper.

6) On the same graph, graph the same point (–1, 2) and draw a line perpendicular to the first line through that point.

7) Write the equation (in standard form) for this new line. (Use the point-slope form y – y1 = m(x – x1).)

What is the equation (standard form)?

8) Write the equation (in slope-intercept form) for this new line.What is the equation (slope-intercept form)?

Parallel and Perpendicular Lines

On the same sheet, copy these statements and fill in the blank.

9) The relationship between the slopes of parallel lines is that _________.

10)The relationship between the slopes of perpendicular lines is that __________.

2-27

11) Find the equation in slope-intercept form and standard form of the line that passes through the point (2, –4) that is parallel to the line 3x – 2y = 5.

12) Find the equation in slope-intercept form and standard form of the line that passes through the point (2, –4) that is perpendicular to the line 3x – 2y = 5.

When you are finished with everything, make sure your name is on the paper and place it on the pile on the gray table.

Finding Equations of Parallel and Perpendicular Lines

Assignment Sec. 2.5: pp. 242-244 (9-12 all, 17-20 all, 25, 26, 28, 47-56 all) Due on Friday, 31 January 2014.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 undefinedWrite 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 book

Write 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

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.