Respuesta :
Answer:
The equation of line perpendicular to given line and passing through point (4 , - 6) is y = - 2 x - 2
Step-by-step explanation:
Given as :
The equation of line is
y = [tex]\dfrac{1}{2}[/tex]x - 3
Now, standard equation of line is
y = m x + c
where m is the slope of line and c is the y-intercept
So, comparing with standard line equation with given line equation
∴ slope of given line = m = [tex]\dfrac{1}{2}[/tex]
Again
other line is perpendicular to given line and passes through point (4 , - 6)
Let The slope of other line = M
∵ Two lines are perpendicular
∴ From perpendicular lines property , the product of lines = - 1
i.e m × M = -1
Or, [tex]\dfrac{1}{2}[/tex] × M = -1
Or M = [tex]\frac{-1}{\frac{1}{2}}[/tex]
∴ M = - 2
So, The slope of other line = M = - 2
Now, equation of line with slope - 2 and points (4 , - 6) in slope-point form
y - [tex]y_1[/tex] = M (x - [tex]x_1[/tex])
Or, y - ( - 6) = ( -2) × (x - 4)
Or, y + 6 = - 2 x + 4
Or, y = - 2 x + 4 - 6
∴ y = - 2 x - 2
So, The equation of other line is y = - 2 x - 2
Hence, The equation of line perpendicular to given line and passing through point (4 , - 6) is y = - 2 x - 2 Answer
