FINDING X AND Y INTERCEPTS AND FINDING EQUATION FROM INTERCEPTS

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.

Finding x and y Intercepts and Finding Equation from Intercepts - Examples

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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