Finding x and y Intercepts and Finding Equation from Intercepts :
Here we are going to see some example problems of finding x and y intercepts and finding the equation of the line from intercepts.
Question 11 :
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 :
(i) 2 and 3
We can find the equation of the line using x and y intercepts, we can use the formula given below.
(x/a) + (y/b) = 1
here "a" stands for x-intercept and "b" stands for y-intercept.
(x/2) + (y/3) = 1
(3x + 2y)/6 = 1
3x + 2y = 6 (or) 3x + 2y - 6 = 0
(ii) -1/3 and 3/2
We can find the equation of the line using x and y intercepts, we can use the formula given below.
(x/a) + (y/b) = 1
here "a" stands for x-intercept and "b" stands for y-intercept.
x/(-1/3) + y/(3/2) = 1
(-3x/1) + (2y/3) = 1
(-9x + 2y)/3 = 1
-9x + 2y = 3
-9x + 2y - 3 = 0
9x - 2y + 3 = 0
Hence the required equation of the line is 9x - 2y + 3 = 0.
(iii) 2/5 and -3/4
a = 2/5 and b = -3/4
x/(2/5) + y/(-3/4) = 1
(5x/2) - (4y/3) = 1
(15x - 8y)/6 = 1
15 x - 8 y = 6
15x - 8y - 6 = 0
Hence the required equation of the line is 15x - 8y - 6 = 0.
Question 12 :
Find the x and y intercepts of the straight line
(i) 5x + 3y - 15 = 0 (ii) 2x - y + 16 = 0 (iii) 3x + 10y + 4 = 0
Solution :
(i) 5x + 3y - 15 = 0
To find the x and y intercepts from the given equation, we have to compare the given equation with the intercept form.
Intercept form of a line :
(x/a) + (y/b) = 1
5x + 3y - 15 = 0
5x + 3 y = 15
Divide the equation by 15
(5x/15) + (3y/15) = 15/15
(x/3) + (y/5) = 1
x-intercept = 3 and y -intercept = 5
(ii) 2x - y + 16 = 0
(x/a) + (y/b) = 1
2x - y = -16
Divide the equation by -16
(2x/(-16)) - (y/(-16)) = -16/(-16)
(x/(-8)) + (y/16) = 1
x-intercept = -8 and y -intercept = 16
(iii) 3x + 10y + 4 = 0
(x/a) + (y/b) = 1
3x + 10y = -4
Divide the equation by -4
(3x/(-4)) + (10y/(-4)) = -4/(-4)
x/(-4/3) + y/(-4/10) = 1
x/(-4/3) + y/(-2/5) = 1
x-intercept = -4/3 and y -intercept = -2/5
After having gone through the stuff given above, we hope that the students would have understood finding x and y intercepts and finding equation from intercepts.
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