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