The Equation of line with points (4 , - 3) and slope 3/2 is y = 3/2 x - 9
Step-by-step explanation:
Given equation of line as :
y =-2/3 x + 6
∵ Standard equation of line is give as
y = a 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 = a = -2/3
Again,
The other line if passing through the points (- 2 , - 1 ) 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 × a = - 1
Or, m × -2/3 = - 1
So, m = -1/-2/3
∴ m = 3/2
Now, Again
The line n is parallel to the line m and passes through the points (4 , - 3)
∵ Line n parallel to line m so, The slope of both are equal
Let The slope of line n is M
So, M = m =
3/2
So, The equation of line written as
y = M x + c
Or, - 3 = 3/2 ( 4 ) + c
Or, - 3 = 3*4/2 + c
Or, - 3 = 6 + c
Or, c = - 3 - 6
∴ c = - 9
So, Equation of line with points (4 , - 3) and slope 3/2 is
y = 3/2 x - 9
Hence , The Equation of line with points (4 , - 3) and slope 3/2 is y = 3/2 x - 9
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