Question

Find the equation of a line: i) whose inclination is 45° and y intercept is 5.
ii) with inclination = 60° and passing through (-2,5). iii) passing
points (-3,1) and (1,5).
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Answer 1

Step-by-step explanation:

(1.) inclination = 45°

∴ slope ( m ) = tan 45°

m = 1;

y intercept ( c ) = 5

equation :

y = mx + c

y = 1.x + 5

y = x + 5;                        ..............(1)

(2.) passing through point = (-2, 5)

inclination = 60°

∴ m = tan 60°

m = √3

equation:

( x - x1 )m = ( y - y1 )

( x - (-2) )√3 = ( y - 5 )

( x + 2 )√3 = ( y - 5 )

√3x + 2√3 = y - 5

√3x = y - 5 - 2√3

x = y - 5 - 2√3 / √3

x - y + 5 = -2√3 / √3

x - y = -2 - 5

x - y = -7                                 .........(2)

(3.) points :

(x1 , y1) = (-3, 1)

(x2, y2) = (1, 5)

m = y2 - y1 / x2 - x1

    = 5 - 1 / 1 - (-3)

    = 4 / 4

    = 1

∴ m = 1;

equation :

( x - x1 )m = ( y - y1 )

( x - 1 ).1 = (y - 5)

x - 1 = y - 5

x + y = 1 - 5

x + y = -4                      ...............(3)

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