math boot camps finding the equation of a line pratice problems with solutions

8/7/2019 Math Boot Camps Finding the Equation of a Line Pratice Problems With Solutions

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Finding the Equation of a Line - Practice Problems with Full Solutions

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Find the equation of the line with the given slope and y-intercept. Write the equation in slope-intercept

form.

1. slope: 3 y-intercept: -1

2. slope:1

2 y-intercept: 4

3. slope:2

3y-intercept: 1

4. slope: 1 y-intercept: 0

5. slope:1

4 y-intercept:

5

6

Find the equation of the line with the given slope which passes through the given point. Write the

equation in slope-intercept form.

6. slope:5

8point: (0, -2)

7. slope: -5 point: (1, 3)


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8. slope: 12

point: (-1, 0)

9. slope: 1 point: (-3, -2)

10.slope:2

3point:

1 1,

2 4

Find the equation of the line which passes through the given points. Write the equation in slope-intercept form.

11. (-1, 2) and (1, 3)

12. (5, 9) and1

,12

13.1 1

,4 2

and1 1

,4 2

14. (-2, -3) and (2, 8)

15. (-1, -1) and (3, 1)

16. (-3, 4) and (1, 0)

17. (4, 0) and (0, 3)


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18. (0, 0) and (4, 6)

19.3

,14

and

1,5

4

20.5 1

,6 4

and

2 1,

3 2

Find the equation of the line with the given graph. Write the equation in slope-interceptform.

21.


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22.

23.


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24.

25.

Mixed Practice

Find the equation of the line given the provided information. Write the equation in slope-interceptform.

26.The line has a slope of1

5and passes through the point (-1, -1).


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27.The line passes through the points1

3,2

and (4, -1).

28.The line passes through the points (0, 1) and (2, -3).

29.The line has an undefined slope and passes through the point (3,3).

30.The line has an x-intercept of -1 and a y-intercept of 2.


3and an x-intercept of -3.

32.The line passes through the points (5, 4) and (0, 0).

33.The line has a slope of 0 and a y-intercept of 5.

34. In standard form, the line is written as1

5 22

x y .


8 and passes through the point

1 1,

8 8

.

Challenge Questions

36.A student says that if you know the line has an undefined slope or a zero slope that there is no

work involved to find the equation of the line. Is this true? Why or why not?

37.Without calculating anything, can you tell if the line passing through the points (-1,5) and (2, 3)

has a positive or a negative slope?


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38. If a line has the same positive number for its x and y intercept, will its slope be positive or

negative?

39.Suppose you know the points (1,4), (2,3), and (4,1) are on a line. Would you get the same

equation if you used to first two points as when you use the last two points? Why or why not?

40. If two lines have the same slope, will they share any points in general?

Solutions

1. Answer: 3 1y x

3, 1m b , 3 ( 1) 3 1 y x y x

2. Answer:1

42

y x

1, 4

2m b . Note: You could also write this answer as 4

2

xy . These are algebraically

the same.

3. Answer:2

13

y x

2, 1

3m b . Note: You could also write this answer as

21

3

xy . These are algebraically the

same.4. Answer: y x

1, 0m b , 1 (0) y x y x

5. Answer:1 5

4 6y x

1 5,

4 6m b . Note: You could also write this answer as

5

4 6

xy . These are algebraically

the same.

6. Answer:5

28

y x

Method 1:

1 1( )

52 ( 0)

8

5 52 2.

8 8

y y m x x

y x

y x y x

Method 2:

5

2 08

52 2

8

y mx b

b

b y x


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7. Answer: 5 8y x

Method 1:

1 1( )

3 5( 1)

3 5 5

5 8

y y m x x

y x

y x

y x

Method 2:

3 5(1)

3 5

8

5 8

y mx b

b

b

b

y x

8. Answer:1 1

2 2y x

Method 1:

1 1( )

10 ( 1 )

2

1 1 11 .

2 2 2

y y m x x

y x

y x y x

Method 2:

1

0 12

10

2

1 1 1

2 2 2

y mx b

b

b

b y x

9. Answer: 1y x

Method 1:

1 1( )

2 1( 3 )

2 3

1

y y m x x

y x

y x

y x

Method 2:

2 1( 3)

2 31

1 1 1

y mx b

b

bb

y x y x

10.Answer:2 7

3 12y x

Method 1:

1 1( )

1 2 1

4 3 2

1 2 2

4 3 6

1 2 1

4 3 3

2 1 1

3 3 4

2 7

3 12

y y m x x

y x

y x

y x

y x

y x

Method 2:

1 2 1

4 3 2

1 2

4 6

1 2 7

4 6 12

2 7

3 12

y mx b

b

b

b

y x


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Note that for the remaining questions, either method above may be used. The solutions will generally

be with the point-slope formula.

11.Answer:1 5

2 2y x

1. Find Slope

2 1

2 1

3 2 1

1 1 2

y ym

x x

2. Find Equation

1 1( )

12 ( 1)

2

12 1

2

1 122 2

1 12

2 2

1 5

2 2

y y m x x

y x

y x

y x

y x

y x

12.Answer:16 1

9 9y x

1. Find Slope

2 1

2 1

1 9 8 28

1 9 95

2 2

16

9

y ym

x x

2. Find Equation

1 1( )

169 5

9

16 809

9 9

16 80 16 80 819

9 9 9 9 9

16 1

9 9

y y m x x

y x

y x

y x x

y x

13.Answer: 2y x

1. Find Slope

2 1

2 1

1 1

1 12 2 21 1 2 1

4 4 4 2

y y

m x x

2. Find Equation


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1 1( )

1

( 1) ( 1)2

11 1

2

1 11

2 2

1 11

2 2

1 1

2 2

y y m x x

y x

y x

y x

y x

y x

16.Answer: 1y x 1. Find Slope

2 1

2 1

0 4 41

1 ( 3) 4

y ym

x x

2. Find Equation

1 1( )

4 1( ( 3))

4 1( 3)

4 3

1

y y m x x

y x

y x

y x

y x

17.Answer:3

34

y x

1. Find Slope

2 1

2 1

3 0 3 3

0 4 4 4

y ym

x x

2. Find Equation

1 1( )

30 ( 4)

4

33

4

y y m x x

y x

y x

18.Answer:3

2y x

1. Find Slope

2 1

2 1

6 0

4 0

y ym

x x

2. Find Equation

1 1( )

30 ( 0)

2

3

2

y y m x x

y x

y x


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19.Answer: 4 4y x

1. Find Slope

2 1

2 1

5 1 4 4 44

1 3 41 3 1

4 4 44 4

y ym

x x

2. Find Equation

1 1( )

31 4

4

31 4

4

1 4 3

4 4

y y m x x

y x

y x

y x

y x

20.Answer:9 21

2 6y x

1. Find Slope2 1

2 1

1 1 1 1 2 1

2 4 2 4 4 42 5 2 5 4 5

3 6 3 6 6 6

3

3 6 18 941 4 1 4 2

6

y ym

x x

2. Find Equation1 1

( )

1 9 5

4 2 6

1 9 45

4 2 12

9 45 1

2 12 4

9 45 3

2 12 12

9 422 12

9 21

2 6

y y m x x

y x

y x

y x

y x

y x

y x


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In the following problems, try to find two points on the graph that are the easiest to work with.

The best choice is the x and y intercepts since they will easily give you the slope! Otherwise look

for nice whole numbers.

21. Answer: 5y x

Graph passes through the points (0,5) and (-5,0)

Slope is rise/run = 5/5 = 1

Since the slope is 1 and the y-intercept is 5 then y=x+5

22.Answer: 2 1y x

Graph passes through the points (0,-1) and (1,1)

Slope is rise/run = 2/1 = 2

Since the slope is 2 and the y-intercept is -1, y=2x-1

5

5

2

1


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23.Answer:1

12

y x

Graph passes through the points (0,1) and (2,0)

Slope is rise/run = -1/2

Slope is -1/2 and the y-intercept is 1 so y=(-1/2)x+1

24.Answer: 3 4y x

Graph passes through the points (-2,2) and (0,-4)

Slope = rise/run = -6/2 = -3

Since the slope is -3 and the y-intercept is -4, y=-3x-4

1

2

6

2


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25.Answer:1 1

4 2y x

Graph passes through the points (-2,-1) and (2,0)

Slope=rise/run = 1 /4

Since the y-intercept isnt clear, we use the point slope formula

1( 1) ( ( 2))

4

11 ( 2)

4

1 214 4

1 11

4 2

1 1

4 2

y x

y x

y x

y x

y x

26.Answer:1 4

5 5y x

Given a point and the slope use point slope formula

4

1


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1( 1) ( ( 1))

5

11 ( 1)5

1 11

5 5

1 11

5 5

1 4

5 5

y x

y x

y x

y x

y x

27.Answer:1

1

2

y x

1. Find Slope

2 1

2 1

1 11 112 2

4 3 1 2

y ym

x x

2. Find Equation

1 1( )

1 1( 3)

2 2

1 1( 3)

2 2

1 1 3

2 2 2

11

2

y y m x x

y x

y x

y x

y x

28.Answer: 2 1y x

2 1

2 1

3 1 42

2 0 2

y ym

x x

The point (0,1) is the y-intercept (Since the y-intercept is the point where x=0) so given the slope

and y-intercept, y=-2x+1

29.Answer: 3x

Any line with an undefined slope will be of the form x=c for a constant c. Since the line passes

through the point (3,3), the x value is 3 so x=3.

30.Answer: 2 2y x

The line passes through the points (-1,0) and (0,2)

2 1

2 1

2 0 22

0 ( 1) 1

y ym

x x


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Since the y-intercept is 2, y=2x+2

31.Answer:2

2

3

y x

m=2/3 and the line passes through the point (-3,0)

2

0 ( 3)3

2( 3)

3

22

3

y x

y x

y x

32.Answer:4

5y x

The point (0,0) is the origin. Any line that passes through the origin is of the form y=mx, so we only

need to find the slope.

2 1

2 1

4 0 4

5 0 5

y ym

x x

33.Answer: 5y

Any line with a slope of zero is of the form y=c where c is a constant.

34.Answer:5 1

2 4y x

To write the answer in point slope form, you have to solve for y

15 2

2

12 5

2

1 5

4 2

x y

y x

y x


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35.Answer:3 11

8 64y x

1 1( )

1 3 1

8 8 8

1 3 3

8 8 64

3 3 1

8 64 8

3 3 8

8 64 64

3 11

8 64

y y m x x

y x

y x

y x

y x

y x

36. Yes! If there is a slope of zero, the equation will be of the form y=c. If there is an undefined

slope, the equation of the line will be of the form x=c where c is a constant.

37.x increased in value (from -1 to 2) while y decreased in value (from 5 to 3) therefore the slope

must be negative.

38. If you try graphing such an example, you can see that it would have a negative slope (in fact it

will be -1 if they are actually the same number)

39. Yes! Only two points are needed to define a line and it doesnt matter which two points are

used.

40.Unless they are the exact same line, they will not share any points. In fact, they will be parrellel.

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