PRACTICE QUESTIONS ON FINDING EQUATIONS OF LINE WITH POINT AND SLOPE

Find the equation of the line from the given point and slope

Questions :

1)  (1, -2) with slope 3

2)  (-4, -1) with slope -2

3)  (5, -2) with slope -3

4)  (5, 2) with slope 1/3

5)  (-2, 8) with slope -1/4

6)  (7, -3) with slope 0

7)  (1, 6) with slope 2/3

8)  (-5, 4) with slope 3/5

9)  (8, 0) with slope -1/4

10) (8, -2) with slope -3/4

11)  (-2, -4) with slope 3

12)  (5, -1) with slope -5

Answers :

1)  y = 3x - 5

2)  y  =  -2x – 9

3)  y  =  -3x + 13

4)  y  =  x/3 + 1/3 

5)  y  = -x/4 + 15/2

6)  y  =  -3

7)  y  =  2x/3 + 16/3   

8)  y  =  3x/5 + 7

9)  y  = -x/4 + 2

10)  y  =  -3x/4 + 4

11)  y  =  3x + 2

12)  y  = -5x + 24 

Solution

Write the equation of the line in standard form 

Problem 1 :

Write the following linear equation in standard form.

y  =  3x + 1

Problem 2 :

Write the following linear equation in standard form.

y  =  x/2 - 3

Problem 3 :

Write the following linear equation in standard form.

y  =  1/4 - 7x/2

Problem 4 :

Write the following linear equation in standard form.

y  =  -5x/4 + 1/6

Solution

Problem 5 :

Find the equation of the straight line whose

(i)  Slope is -4 and passing through (1, 2).

(ii)  Slope is 2/3 and passing through (5, -4).

Problem 6 :

Find the equation of the straight line which passes through the midpoint of the line segment joining

(4, 2) and (3, 1)

whose angle of inclination is 30 degree.

Solution

Problem 7 :

Find the equation of the line in the xy-plane with slope −4 that contains the point (−5,−2).

Problem 8 :

Find the equation of the line that contains the points (2,−1) and (4, 9).

Problem 9 :

Find the equation of the line that contains the points (−3, 2) and (−5, 7).

Solution

Problem 10 :

Find the equation of a straight line whose slope is 7 and which passes through the point (5,-6).

Problem 11 :

Find the equation of a straight line whose slope is 6 and which passes through the point (-1, -2) 

Problem 12 :

Find the equation of a straight line whose slope is 2/3 and which passes through the point (-2,-4) 

Problem 13 :

Find the equation of a straight line whose slope is -1/5 and which passes through the point (-3,-1) 

Problem 14 :

Find the equation of a straight line whose slope is -2/7 and which passes through the point (-5,-4) 

Solution

Problem 15 :

Find the equation of a straight line whose slope is 5 and which passes through the point (1, -3)

Problem 16 :

Find the equation of a straight line whose slope is -1/5 and which passes through the point (4, 8)

Problem 17 :

Find the equation of a straight line whose slope is 1/7 and which passes through the point (-1,8)

Problem 18 :

Find the equation of a straight line whose slope is 2/5 and which passes through the point (0,-7)

Problem 19 :

Find the equation of a straight line whose slope is 5/7 and which passes through the point (-2,-1)

Solution

Answers :

1)  3x - y  =  -1

2)  x - 2y  =  6

3)  14x + 4y  =  1

4)  15x + 12y  =  2

5)  2x–3y–22  =  0

6)  2x-2√3y-7+3√3  =  0

7)  4x + y + 22  =  0

8)  5x - y - 11  =  0

9)  5x + 2y + 11  =  0

10)  7x + y + 41  =  0

11)  6x - y + 4  =  0

12)  2x - 3 y + 16  = 0

13)  x + 5 y + 8 = 0

14)  2 x + 7 y + 38  =  0

15)  5x - y - 8  =  0

16)  x - 5 y - 44  =  0

17)  x - 7y + 57  =  0 

18)  2x - 5y - 35  =  0

19)  5 x - 7 y + 3  =  0

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