unit 1: linear equations - tcann - home1+-+linear...intermediate algebra unit 1: linear equations 12...

Intermediate Algebra Unit 1: Linear Equations x

y

Intermediate Algebra Unit 1: Linear Equations

1

Objectives: page

locate, label, and state ordered pairs and the four quadrants 2

state and identify the four types of slope: positive, negative, zero, and no slope 3

calculate the slope of a line given two points 4

write a linear equation in slope-intercept form given two points 5 – 6

transform a linear equation into slope-intercept form and graph 7

write a linear equations of parallel and perpendicular lines 8 – 13

find the x- and y-intercepts of linear equations 14 – 16

review questions 17 – 22


2

Graphing With Ordered Pairs: Use the accompanying graph grid to answer the following questions:

State the coordinates of the indicated point:

(1) A

(2) I

(3) H

(4) C

(5) E

(6) N

Name the letter of each ordered pair: (7) (-2, 6)

(8) (0, -3)

(9) (5, -5)

(10) (-1, -1)

(11) (-7, -8)

(12) (7, -1)

(13) Where the x- and y-coordinates are equal

(14) Where the y-coordinate is three times the value of the x-coordinate

Name the quadrant or the axis on which each point lies: (15) (-4, 3)

(16) (0, 6)

(17) (4, -2)

(18) (-1, -1)

(19) (-2, 0)

(20) (1, 2)


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Slope:

(work space for next page)


4


5

Writing & Graphing Linear Equations:



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7

Graphing Using Slope-Intercept Form:

(1) y = 2x – 4 (2) 1x

3

2y

(3) 3x – y = 7 (4) 2x + 3y = 6

(5) x – 4y + 8 = 0 (6) 6x – 5y = 15

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y

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y

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Parallel Lines:

Perpendicular Lines:

For questions (1) – (6), write an equation in slope-intercept form that passes through the given point and is PARALLEL to the graph of the given equation:

(1) y = -2x + 5 (3, 1) (2) y = 3x – 5 (-1, -2)

(3) 5x3

4y (12, 3) (4)

4

1x

4

3y (4, -2)

(5) 5x – 4y = 1 (-8, 2) (6) x – 3y = 8, with a y-intercept of -6


9

For questions (7) – (12), write an equation in slope-intercept form that passes through the given point and is PERPENDICULAR to the graph of the given equation:

(7) 4x4

1y (-2, 3) (8)

3

1x

6

1y (2, 4)

(9) y = 2x + 5 (-2, 9) (10) 4x + 3y = -6 (2, 1)

(11) x = 2y – 1 (0, 0) (12) 5x – 3y = 2, with an x-intercept of 3


10

Parallel & Perpendicular Lines:

Write a linear equation in slope-intercept form that passes through:

(1) the point (4, 6) and is parallel to the line 5x3

2y

(2) the point (2, -5) and is perpendicular to the line 7x4

1y

(3) the point (-5, 6) and is perpendicular to the line 3y5

1x3


11

Writing Linear Equations: (1) Write an equation of a line whose slope is -¾ and y-intercept is -5.

(2) Write an equation of a line whose y-intercept is 1 and slope is -1.

(3) Write an equation of a line whose slope is zero and y-intercept is 6.

(4) Which of the following lines is parallel to the line whose equation is 3y = 4x + 8?

(1) y = 4x – 5 (2) y = 3x + 8 (3) 1x4

3y (4) 5x

3

4y

(5) Which of the following lines is perpendicular to the line whose equation is 6x + 7y = 14?

(1) 7y = -6x – 7 (2) 9x6

7y (3) 7x + 6y = 14 (4) 12x + 14y = 28

(6) Write an equation of a line whose slope is ½ and passes through the point (-4, 1).

(7) Write an equation of a line whose slope is -⅔ and passes through the point (-3, 7).


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(8) Write an equation of a line that is perpendicular to the line y = ½x – 4 and passes through the point (4, 6).

(9) Write an equation of a line that is parallel to the line y = ½x + 5 and passes through the point (-10, 1).

(10) Write an equation of a line that is perpendicular to the line 3x + 4y = 0 and passes through the point (-3, 7).

(11) Write an equation of a line that is perpendicular to the line 5y = -2x + 10 and passes through the point (4, 3).

(12) Write an equation of a line that is parallel to the line 3y = 2x + 7 and passes through the point (-3, 5).

(13) Write an equation of a line that is parallel to the line 5x + 4y = 16 and passes through the point (1, 2).


13

(14) Write an equation of a line that passes through the points (5, -4) and (2, 2).

(15) Write an equation of a line that passes through the points (-2, 5) and (1, 3).

(16) Write an equation of a line that passes through the points (3, 2) and (6, 3).


14

X- and Y-Intercepts:

Find the x- and y-intercepts for each linear equation: (1) x-intercept: y-intercept:

(2) x-intercept: y-intercept:


(4) Given the equation 2x + 3y = 6, find the x- and y-intercepts: (a) graphically (b) algebraically

x

y


15

x

y

x

y

x

y

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State and use the x- and y-intercepts to graph each linear equation:

(11) 3x + 2y = -6 (12) x – 4y = 4

(13) y = 0.5x – 1 (14) ⅓x + y = 1


16

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x

y

x

y

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Algebraically find the x- and y-intercepts for each linear equation:

(15) 3x + 4y = 12 (16) 2x – 2y = -4 (17) 5x – 3y = 15

(18) y = 4x + 2 (19) y = -3x – 9 (20) 4x – 2y – 8 = 0

State and use the x- and y-intercepts to graph each linear equation:

(21) 6x + 3y = -18 (22) -5x + y = 5

(23) 2x – 5y = 0 (24) 4x + 2y = 8


17

Review Questions: State the slope of each line:

(1) a (2) b

(3) c (4) d

(5) e (6) f

(7) g (8) h

(9) i (10) j

Find the slope of the line that passes through the two given points:

(11) (2, 5) and (3, 6) (12) (4, 1) and (-4, 1) (13) (4, 1) and (-6, -4)

(14) (-2, 4) and (10, 0) (15) (3, 2) and (3, -2) (16) (2, 7) and (-2, -3)


18

Algebraically find the value of r so the line that passes through the two points has the given slope:

(17) (6, 3), (r, 2), 2

1m (18) (r, 3), (-4, 5),

5

2m

(19) (5, r), (2, -3), 3

4m (20) (-2, 7), (r, 3),

3

4m

(21) (4, -5), (3, r), 8m (22) (6, 2), (9, r), 1m

(23) (4, r), (r, 2), 3

5m (24) (r, 5), (-2, r),

9

2m


19

Review Questions: For each line graphed below, complete the given table:

slope x- and y-intercepts

linear equation in slope-intercept form

(1) r

(2) s

(3) t

Algebraically find the x- and y-intercepts for each linear equation:

(4) 4x – 3y = 12 (5) 2x – 5y = 20 (6) x + 5y = 8 (7) 3x – y = -7

State the slope and y-intercept of each linear equation:

(8) 5x + 2y = 7 (9) -2x + 3y = 8 (10) 8x – y = 12 (11) 7x – 2y = 9


20

Write the linear equation in slope-intercept form that passes through each of the two given points:

(12) (3, 4) and (-1, -4) (13) (2, 5) and (0, 3)

(14) (-3, 1) and (-1, -3) (15) (-5, -2) and (1, -6)

(16) (-5, 3) and (4, 3) (17) (-2, 4) and (-2, -2)


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unit 1: linear equations - tcann - home1+-+linear...intermediate algebra unit 1: linear equations 12...

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