Equation of line Solution10



In this page equation of line solution10 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(1) Find the slope of the straight line

(i) 3x + 4 y – 6 = 0

Solution:

To find the slope of the given equation we have to use the following formula

         Slope (m) = - coefficient of x/coefficient of y

                     m = -3/4


(ii) y = 7 x + 6

Solution:

To find the slope of the given equation we have to compare the given equation with the equation y = m x + b

                y = 7 x + 6

                m = 7


(iii) 4x = 5 y + 3

Solution:

To find the slope of the given equation we have to use the following formula

         Slope (m) = - coefficient of x/coefficient of y

For that we have to change this equation in the form a x + b y + c = 0

4 x – 5 y – 3 = 0

    m = - (-5)/4

m = 5/4


(2) Show that the straight lines x + 2 y + 1 = 0 and 3 x + 6 y + 2 = 0 are parallel.

Solution:

If two lines are parallel then

Slope of the first line (m1) = Slope of the second line (m2)

m = coefficient of x/coefficient of y

Slope of the first line (m1) = -1/2

Slope of the first line (m2) = -3/6

                                           = -1/2

                              m1 = m2

Therefore we can say the given two lines are parallel.


(3)Show that the straight lines 3 x – 5 y + 7 = 0 and 15 x + 9 y + 4 = 0 are perpendicular

Solution:

If two lines are perpendicular then

Slope of the first line (m1) x Slope of the second line (m2) = -1

m = coefficient of x/coefficient of y

m1 = -3/(-5)

      = 3/5

m2 = -15/9

      = -5/3

(3/5) x (-5/3) = -1

                 -1 = - 1   

Therefore we can say the given two lines are perpendicular.

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