# EQUATION OF LINE WORKSHEET

## About "Equation of Line Worksheet"

Equation of Line Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on finding the equation of a line.

Before look at the worksheet, if you would like to know the basic stuff about finding the equation of a line,

## Equation of Line Worksheet - Problems

Problem 1 :

Find the general equation of a line whose slope is 3 and y-intercept is 4.

Problem 2 :

Find the general equation of a line passing through the point (3, 0) with slope -6.

Problem 3 :

Find the general equation of a line passing through the point (2, 5) with slope -5.

Problem 4 :

Find the general equation of a line passing through the points (-1, 1) and (2, -4).

Problem 5 :

If the x-intercept and y-intercept of a line are 2/3 and 3/4 respectively, find the general equation of the line.

Problem 6 :

Find the equation of a line which is parallel to x-axis and passing through the point (2, 3).

Problem 7 :

Find the general equation of a line which is parallel to the line 3x −7y  =  12 and passing through the point (6, 4).

Problem 8 :

Find the equation of a line which is perpendicular to the line

y  =  4/3 ⋅ x − 7

and passing through the point (7, –1). ## Equation of Line Worksheet - Solutions

Problem 1 :

Find the general equation of a line whose slope is 3 and y-intercept is 4.

Solution :

Equation of a line in slope-intercept form :

y  =  mx + b

Substitute 3 for m and 4 for b.

y  =  3x + 4.

Subtract y from each side.

0  =  3x - y + 4

or

3x - y + 4  =  0

So, the general equation of the required line is

3x - y + 4  =  0

Problem 2 :

Find the general equation of a line passing through the point (3, 0) with slope -6.

Solution :

Given : A point and slope

So, the equation of the straight line in point-slope form is

y - y1  =  m(x - x1)

Substitute (x1 , y1) = (3 , 0) and m = -6.

y - 0  =  -6(x - 3)

Simplify.

y  =  -6x + 18

Add 6x to each side.

6x + y  =  18

Subtract 18 from each side.

6x + y - 18  =  0

So, the general equation of straight line is

6x + y - 18 = 0

Problem 3 :

Find the general equation of a line passing through the point (2, 5) with slope -5.

Solution :

In this problem, instead of using point-slope form, we can use slope-intercept form also to find the equation of the line.

y  =  mx + b

Substitute m  =  -5.

y  =  -5x + b ----(1)

Substitute (x, y)  =  (2, 5)

5  =  -5(2) + b

Simplify.

5  =  -10 + b

Add 10 to each side.

15  =  b

Substitute 15 in (1).

(1)---->  y  =  -5x + 15

Add 5x to each side.

5x + y  =  15

Subtract 15 from each side.

5x + y - 15  =  0

So, the general equation of straight line is

5x + y - 15 = 0

Problem 4 :

Find the general equation of a line passing through the points (-1, 1) and (2, -4).

Solution :

Given : Two points on the straight line : (-1, 1) and  (2, -4).

So, the equation of the straight line in two-points form is

(y - y₁) / (y₂ - y₁)  =  (x - x₁) / (x₂ - x₁)

Substitute (x1 , y1)  =  (-1, 1) and (x2, y2)  =  (2, -4).

(y - 1) / (-4 - 1)  =  (x + 1) / (2 + 1)

Simplify.

(y - 1) / (-5)  =  (x + 1) / 3

Cross multiply.

3(y - 1)  =  -5(x + 1)

3y - 3  =  -5x - 5

5x + 3y + 2  =  0

Hence the general equation of the required line is

5x + 3y + 2  =  0

Problem 5 :

If the x-intercept and y-intercept of a line are 2/3 and 3/4 respectively, find the general equation of the line.

Solution :

Given :

x- intercept  "a"  =  2/3

y-intercept  "b"  =  3/4

So, the equation of the straight line in intercept form is

x/a  +  y/b  =  1

Substitute a  =  2/3  and  b  =  3/4.

x / (2/3)  +  y / (3/4)  =  1

Simplify.

3x/2  +  4y/3  =  1

(9x + 8y)  / 6  =  1

Multiply each side by 6.

9x + 8y  =  6

Subtract 6 from each side from 6.

9x + 8y - 6  =  0

So, the general equation of the required line is

9x + 8y - 6  =  0

Problem 6 :

Find the equation of a line which is parallel to x-axis and passing through the point (2, 3).

Solution :

Equation of a line parallel to x-axis :

y  =  k -----(1)

The above line is passing through (2, 3).

So, substitute (x, y)  =  (2, 3).

3  =  k

Substitute k  =  3 in (1).

y  =  3

So, the equation of the required line is

y  =  3

Problem 7 :

Find the general equation of a line which is parallel to the line 3x −7y  =  12 and passing through the point (6, 4).

Solution :

Equation of a line parallel to 3x - 7y  =  12  :

3x - 7y + k  =  0 ----- (1)

The above line is passing through (6, 4).

So, substitute (x, y)  =  (6, 4).

3(6) - 7(4) + k  =  0

Simplify.

18 - 28 + k  =  0

-10 + k  =  0

Add 10 to each side.

k  =  10

Substitute k  =  10 in (1).

(1)-----> 3x - 7y + 10  =  0

So, the general equation  of the required line is

3x - 7y + 10  =  0

Problem 8 :

Find the equation of a line which is perpendicular to the line

y  =  4/3 ⋅ x − 7

and passing through the point (7, –1).

Solution :

Write the equation y  =  4/3 ⋅ x − 7 in general form.

y  =  4/3 ⋅ x − 7

Multiply each side by 3.

3y  =  4x - 21

Subtract 3y from each side.

0  =  4x - 3y - 21

or

4x - 3y - 21  =  0

Equation of a line perpendicular to 4x - 3y - 21 = 0.

3x + 4y + k  =  0 ----- (1)

The above line is passing through (7, -1).

So, substitute (x, y)  =  (7, -1).

3(7) + 4(-1) + k  =  0

Simplify.

21 - 4 + k  =  0

17 + k  =  0

Subtract 17 from each side.

k  =  -17

Substitute k  =  -17 in (1).

(1)-----> 3x + 4y - 17  =  0

So, the general equation  of the required straight line is

3x + 4y - 17  =  0 After having gone through the stuff given above, we hope that the students would have understood, "Equation of Line Worksheet".

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