EQUATIONS OF STRAIGHT LINES WORKSHEET

Problem 1 :

Find the general form of equation of a straight line whose slope is 3 and y-intercept -2. 

Problem 2 :

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

Problem 3 :

Find the general equation of the straight line passing through the point (-2, 3) with slope 1/3.

Problem 4 :

Find the general equation of the straight line whose x-intercept -2 and y-intercept is 3.

Problem 5 :

Find the equation of a straight line parallel to y-axis and passing through (-5, 0).

Problem 6 :

Find the equation of a straight line parallel to x-axis and passing through (0, 6).

Problem 7 :

Find the equation of a straight shown below in slope-intercept form. 

Problem 8 :

Find the equation of a straight shown below in slope-intercept form. 

Answers

1. Answer :

Given : Slope  m = 3 and y-intercept b = -2.

Equation of the straight line in slope-intercept form : 

y  =  mx + b

Substitute m = 3 for m and b = -2.

y  =  3x - 2

Subtract y from each side.

0  =  3x - y - 2

or

3x - y - 2  =  0

2. Answer :

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

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

3. Answer :

Given : Point  =  (-2, 3)  and  slope  m  =  1/3

Equation of the straight line in point-slope form is

y - y1  =  m(x - x1)  

Substitute (x1 , y1) = (-2 , 3) and m = 1/3. 

y - 3  =  1/3 ⋅ (x + 2)

Multiply each side by 3.

3(y - 3)  =  x + 2

Simplify. 

3y - 9  =  x + 2

Subtract 3y from each side. 

-9  =  x - 3y + 2

Add 9 to each side.

0  =  x - 3y + 11

or

x - 3y + 11 = 0

4. Answer :

Given : x-intercept is -2  and y-intercept is 3.

Equation of the straight line in intercept-form is 

x/a + y/b  =  1

Substitute a = -2 and b = 3. 

x/(-2) + y/3  =  1 -----(1)

The lest common multiple of (2, 3) is 6.

So, multiply each side (1) by 6. 

-3x + 2y  =  6

Multiply each side by -1.

3x - 2y  =  -6

Add 6 to each side. 

3x - 2y + 6  =  0

5. Answer :

Equation of a straight parallel to y-axis is 

x  =  c

It is passing through the point (-5, 0)

Then, 

-5  =  c

So, the equation of the given line is 

x  =  -5

or

x + 5  =  0

6. Answer :

Equation of a straight parallel to x-axis is 

y  =  k

It is passing through the point (0, 6)

Then, 

6  =  k

So, the equation of the given line is 

y  =  6

or

x + 5  =  0

7. Answer :

The above line is a falling line. So, its slope will be a negative value.

Measure the rise and run. 

For the above line, 

Rise  =  1

Run  =  4

Then, 

Slope  =  rise / run

Slope  =  -1/4

From the graph shown above y-intercept is -1. 

Equation of a straight line in slope-intercept form is

y  =  mx + b

Substitute m = -1/4 and b = -1. 

y  =  (-1/4)x - 1

y  =  -x/4 - 1

8. Answer :

The above line is a falling line. So, its slope will be a positive value.

Measure the rise and run. 

For the above line, 

Rise  =  6

Run  =  2

Then, 

Slope  =  rise / run

Slope  =  6/2

Slope  =  3

From the graph shown above y-intercept is -2. 

Equation of a straight line in slope-intercept form is

y  =  mx + b

Substitute m = 3 and b = -2. 

y  =  3x - 2

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