Note: The equation of a line having slope of and as is given by

Question 1: Find the equation of a line making an angle of with the x-axis and cutting off an intercept from y-axis

Answer:

Given:

Substituting in we get

Hence the equation of the line is

Question 2: Find the equation of a straight line:

(i) with slope and y-intercept

(ii) with slope and y-intercept

(iii) with slope and intersecting the x-axis at a distance of units to the left of origin.

Answer:

i) Given

Substituting in we get

Hence the equation of a straight line with slope and y-intercept is

ii) Given

Substituting in we get

Hence the equation of a straight line with slope and y-intercept is

iii) Given and passes through

Substituting in we get

Substituting in we get the equation of the line is

Hence the equation of a straight line with slope and passes through is

Question 3: Find the equations of the bisectors of the angles, between the coordinate axes.

Answer:

For line 1,

Substituting in we get the equation of line 1 is

For line 2,

Substituting in we get the equation of line 2 is

Hence the equations of the bisectors of the angles, between the coordinate axes

Question 4: Find the equation of a line which makes an angle of with the x-axis and cuts off an intercept of units on negative direction of y-axis.

Answer:

Here

Substituting in we get the equation as

Hence the equation of a line which makes an angle of with the x-axis and cuts off an intercept of units on negative direction of y-axis is

Question 5: Find the equation of a line that has y-intercept and is parallel to the line joining and .

Answer:

Here slope

Substituting in we get the equation as

Hence equation of a line that has y-intercept and is parallel to the line joining and is

Question 6: Find the equation of a line which is perpendicular to the line joining and and cuts off an intercept of length on y-axis.

Answer:

Slope of line joining and

The slope of the required line, which is to the above line

Substituting in we get the equation as

Hence the equation of the required equation is

Question 7: Find the equation of the perpendicular to the line segment joining and if it cuts off an intercept from y-axis.

Answer:

Slope of line joining and

The slope of the required line, which is to the above line

Substituting in we get the equation as

Hence the equation of the required equation is

Question 8: Find the equation of the straight line intersecting y-axis at a distance of units above the origin and making an angle of with the positive direction of the x-axis

Answer:

Here

Substituting in we get the equation as

Hence the equation of the required equation is