Chapter 6

Equations of a line

1. Determine the slope of this line segment.

0

A

B

2 4–2–4 x

2

4

–2

–4

y

Slope = Run

Rise

6

-4

4

6

2

3

2. Is the slope of this line segment positive, negative, zero, or not defined?

0

S

T

4 8–4–8 x

4

8

–4

–8

y Slope = Run

Rise

0

6

Not Defined

3. Determine the slope of a line that is perpendicular to the line through W(–9, 7) and X(6, –10).

4. For a service call, a plumber charges a $95 initial fee, plus $45 for each hour he works. Write an equation to represent the total cost, C dollars, for t hours of work.

WX - Slope = )(

)(

12

12

xx

yy

)9(6

710

15

17

C = 45t + 95

17

15 slope

5. Write an equation to describe this graph.

0 2 4–2–4 x

2

4

–2

–4

y y = mx + b b =m =

-1

5

1

1-5

y = x – 15

1

y – y1= m(x – x1)

y – (-2)= (x – 5)5

1

y + 2 = (x – 5)5

1

6. Describe the graph of the linear function with this equation:

)2(3

13 xy

Slope =

Point =

3

1

(2, -3)

7. Which graph represents the equation

a) c)

b) d)

)3(4

31 xy

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

0 2 4–2–4 x

2

4

–2

–4

y

m =

p =

4

3

(-3, -1)

8. Write this equation in slope-intercept form: First Method

)2(5

13 xy y = mx + b

xy5

13

5

2

33

35

2

5

1 xy

35

2

1

3

5

2

5

15

5

2

x5x5

5

135

13

5

1 xy

8. Write this equation in slope-intercept form: Second Method

)2(5

13 xy

Slope =

)2(5

13 y

5

23 y

33

35

2y

35

2

1

3

5

2

5

15

5

2

x5x5

5

13

5

13

5

1 xy

- 1/5y – intercept:

)20(5

13 y

9. Determine the y-intercept of the graph of this equation: )5(43 xy

y-intercept = 23(0,23)

)50(43 y)5(43y

203y320y

23y

10. Write an equation in slope-point form for the line that passes through A(–2, 4) and B(–9, 6).

y – y1= m(x – x1)

m = )(

)(

12

12

xx

yy

)2(9

46

7

2

x1 y1 x2 y2

y – 4= (x + 2)7

2

or

y – 6= (x + 9)7

2

11. Write an equation for the line that passes through T(–3, 3) and is parallel to the line a) In point-slope form

b) In slope-intercept form

c) In general form

107 xy

Parallel m = 7

y – y1= m(x – x1)

y – 3= 7(x + 3)

y – 3= 7(x + 3)y – 3= 7x + 21

y = 7x + 21 +3y = 7x + 24

y = 7x + 24 – y – y 0 = 7x – y + 24 7x – y + 24 = 0

12. Write this equation in general form:

)3(3

55 xy

)3(5153 xy

15xy 5153

1515

3053 xy

30350 yx

3( )

yy 33

03035 yx

13. Determine the slope of the line with this equation:

0537 yx-7x -7x

xy 753 -5 -5

573 xy3 3 3

3

5

3

7 xy

3

7m

14. The coordinates of the endpoints of segments are given below. State whether they are parallel, perpendicular, or neither?

R(–2, 8), S(–12, –4) and T(3, –1), U(9, 4)

mRS = )(

)(

12

12

xx

yy

)2(12

84

10

12

5

6

mTU = )(

)(

12

12

xx

yy

39

)1(4

6

5

Neither

15. Determine the x- and y-intercepts of the graph of this equation: 5x +8y + 40 = 0

x-intercept y = 0

5x + 8(0) + 40 = 05x + 40 = 0

-40 -405x = -405 5

x = -8

y-intercept x = 0

5(0) + 8y + 40 = 08y + 40 = 0

-40 -408y = -408 8

y = -5

16. Write an equation, in slope-point form, for the line that passes through B(–2, 5) and is:a) parallel to the line

b) perpendicular to the line 22

5 xy 2

2

5 xyy – y1= m(x – x1)

2

5y – 5= (x + 2)

5

2y – 5= (x + 2)