Equation of line Solution8



In this page equation of line solution8 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(16) Find the equation of the line passing through the point (9,-1) and having its x-intercept thrice and its y-intercept.

Solution:

Let "a" and "b" are x and y-intercepts respectively.

x - intercept (a) = 3 (y-intercept)

                    a = 3 b

The required line is passing through the point (9 , -1)

(x/a) + (y/b) = 1

(9/3b) - (1/b) = 1

(9 - 3)/3b = 1

6/3b = 1

2/b = 1

2 = b

y-intercept (b) = 2

x -intercept (a) = 3(2) = 6

(x/6) + (y/2) = 1

(x/6) + (3y/6) = 1

x + 3 y = 6

x + 3y - 6 = 0            


(17) A straight line cuts coordinate axes at A and B. If the midpoint of AB is (3,2), then find the equation of AB.

Solution:

Let x -intercept be "a" and y-intercept be "b"

So the coordinate of A is (a , 0) and coordinate of B is (0 , b)

Midpoint of AB = (x₁ + x₂)/2 , (y₁ + y₂)/2

           (3 , 2) = (a + 0)/2 , (0 + b)/2

           3 = a/2       2 = b/2

           a = 6          b = 4

Intercept form:

(x/a) + (y/b) = 1

(x/6) + (y/4) = 1

(2 x + 3 y)/12 = 1

2 x + 3 y = 12

2 x + 3 y - 12 = 0  equation of line solution8  equation of line solution8


(18) Find the equation of the line passing through (22,-6) and having intercept on x-axis exceeds the intercept on y-axis by 5.

Solution:

Let x -intercept be "a" and y-intercept be "b"

x -intercept (a) = b + 5

Intercept form:

(x/a) + (y/b) = 1

(22/(b+5)) + (-6/b) = 1

[22 b - 6(b+5)]/b(b+5) = 1

(22 b - 6 b - 30)/b² + 5b = 1

(16 b - 30)/b² + 5b = 1

16 b - 30 = b² + 5b

b² + 5 b - 16 b  - 30 = 0

b² - 11 b  - 30 = 0

(b - 6) (b - 5) = 0

b = 6 and b = 5

a = 6 + 5         a = 5 + 5

a = 11             a = 10

a = 11 , b = 6

(x/11) + (y/6) = 1

6 x + 11 y = 66

6 x + 11  y - 66 = 0

a = 10 , b = 5

(x/10) + (y/5) = 1

 x + 2 y = 10

x + 2 y - 10 = 0

The required equations are x + 2 y - 10 = 0 or 6 x + 11  y - 66 = 0

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