x-intercept :
It is the point where a line crosses the x-axis.
y-intercept :
It is the point where a line crosses the y-axis.
Example 1 :
Find the equation of the straight line whose x and y-intercepts on the axes are given by
(i) 2 and 3
(ii) -1/3 and 3/2
(iii) 2/5 and -3/4
Solution :
Part (i) :
To find the equation of the line whose x and y-intercepts are a and b we have to use the following formula.
x/a + y/b = 1
Here, x -intercept (a) = 2 and y -intercept (b) = 3.
x/2 + y/3 = 1
(3x + 2y)/6 = 1
3x + 2y = 6
3x + 2y - 6 = 0
Part (ii) :
-1/3 and 3/2
Here, x-intercept (a) = -1/3 and y-intercept (b) = 3/2.
x/(-1/3) + y/(3/2) = 1
-3x + 2y/3 = 1
(-9x + 2y)/3 = 1
-9x + 2y = 3
9x - 2y + 3 = 0
Part (iii) :
2/5 and -3/4
x/a + y/b = 1
Here, x-intercept (a) = 2/5 and y -intercept (b) = -3/4.
x/(2/5) + y/(-3/4) = 1
5x/2 - 4y/3 = 1
(15x - 8y)/6 = 1
15x - 8y = 6
15x - 8y - 6 = 0
Example 2 :
Find the equation of the straight line whose x and y-intercepts on the axes are given by.
(i)
Solution :
x-intercept = 4 and y-intercept = -3
Equation of the line :
x/a + y/b = 1
x/4 + y/(-3) = 1
x/4 - y/3 = 1
(3x - 4y)/12 = 1
3x - 4y = 12
3x - 4y - 12 = 0
(ii)
Solution :
x-intercept = 5 and y-intercept = -5
Equation of the line :
x/a + y/b = 1
x/5 + y/(-5) = 1
x/5 - y/5 = 1
(x - y)/5 = 1
x - y = 5
x - y - 5 = 0
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