Question 1
Question: Find the equation of the line which makes intercepts of 3 and 5 with x-axis and y-axis respectively.
Answer: Here, a = 3, b = 5.
Question 2
Question: Find the equation of the line through (4,6) and the sum of the intercepts on the coordinate axis is 20.
Answer: Let a be the intercept on the x-axis, then 20 - a is the intercept on the y-axis.
The equation of the line is
This line passes through (4,6).
When a = 8, b = 12 and when a = 10, b = 10.
The equation of the line is
Question 3
Question: A straight line moves so that the sum of reciprocals of intercepts on the axes of coordinates is constant. Show that it will pass through a fixed point.
Answer: Let the equation of the line in the intercept form be
From the problem, we have
Question 4
Question: The part of line intercepted between the axes is divided by the point (-5,2) in the ratio 2:3. Find the equation of the line.
Answer: 
Then, the intercepts made by the line on the x-axis is a and on y-axis is b.
P divides the line joining the point A(a,0) and B(0,b) in the ratio AP : PB::2 : 3.
Question 5
Question: Find the equation of the straight line passing through the point (3,-4) and cutting off equal intercepts but of opposite signs from the axis.
Answer: Let the equation of the line in the intercept form be
From the problem, (a,-a) are the intercepts.
This line passes through (3,-4).
Question 6
Question: Find the equation of the line passing through (-2,4) and whose intercepts on x-axis is thrice as that on the y-axis.
Answer: Let the equation of the line in the intercept form be
The intercepts on the axes are a and b. But a = 3b.
This line passes through (-2,4).
Question 7
Question: Find the equation of the straight line which passes through (-3,5) and cuts the axes at A and B, so that OA + OB = 4, where O is the origin.
Answer: 
Let the equation of the line in the intercept form be
From the problem a + b = 4, b = 4 - a
This line passes through (-3,5).
\ a 
- 6 or a 
2
When a = - 6, b = 4 - (-6) = 10
When a = 2, b = 4 - 2 = 2
Line is x + y = 2.
Question 8
Question: Find the equation of the straight line whose intercepts on x and y axes are respectively twice and thrice of those made by the line 3x - 4y = 12.
Answer: Given line is 3x - 4y = 12.
Now put y = 0 to get x-intercept.
3x = 12y
3x = 12(0)
x = 4
\ a = 4
Next, put x = 0 to obtain y-intercept.
The intercepts made by the new required line are
a = 2(4), b = 3(-3) = -9.
Question 9
Question: Find the ratio in which the straight line 2x + 3y - 5 = 0 divides the line joining two points (-4,1) and (2,7).
Answer: Let m:n be the ratio in which the line divides the line joining the points (-4,1) and (2,7).
Question 10
Question: Find the equation of the straight line passing through the origin and the middle point of the intercept of the line ax + by + c = 0 between the axes.
Answer: Given line is ax + by + c = 0.
The equation of line is
