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Answer:
The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0
The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0
Step-by-step explanation:
Given equation of line as :
5 x + 2 y = 12
or, 2 y = - 5 x + 12
or , y = x +
Or, y = x + 6
∵ Standard equation of line is give as
y = m x + c
Where m is the slope of line and c is the y-intercept
Now, comparing given line equation with standard eq
So, The slope of the given line = m =
Again,
The other line if passing through the points (- 2 , 3 ) And is parallel to given line
So, for parallel lines condition , the slope of both lines are equal
Let The slope of other line = M
So, M = m =
∴ The equation of line with slope M and passing through points ( -2 , 3) is
y = M x + c
Now , satisfying the points
So, 3 = × ( - 2 ) + c
or, 3 = + c
Or, 3 = 5 + c
∴ c = 3 - 5 = - 2
c = - 2
So, The equation of line with slope and passing through points ( -2 , 3)
y = x - 2
or, 2 y = - 5 x - 4
I.e 5 x + 2 y + 4 = 0
<u>Similarly</u>
The other line if passing through the points (- 2 , 3 ) And is perpendicular to given line
So, for perpendicular lines condition,the products of slope of both lines = - 1
Let The slope of other line = M'
So, M' × m = - 1
Or, M' × = - 1
Or, M' =
Or, M' =
∴ The equation of line with slope M and passing through points ( -2 , 3) is
y = M' x + c'
Now , satisfying the points
So, 3 = × ( - 2 ) + c'
or, 3 = + c'
Or, 3 × 5 = - 4 + 5× c'
∴ 5 c' = 15 + 4
or, 5 c' = 19
Or, c' =
So, The equation of line with slope and passing through points ( -2 , 3)
y = x +
y =
Or, 5 y = 2 x + 19
Or, 2 x - 5 y + 19 = 0
Hence The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0
And The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0
Answer