Note: The equation of a line having slope of 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:

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:

we get

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

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

and passes through

we get

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:

we get the equation of line 1 is

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:

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 .

Answer:

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

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

Answer:

Hence the equation of the required equation is

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

Answer:

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:

we get the equation as

Hence the equation of the required equation is