Write the equation of the line that is parallel to y= 3x -7 and goes through point (4,2).
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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 = 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 =
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
∴ <u>From perpendicular lines property , the product of lines = - 1</u>
i.e m × M = -1
Or, × M = -1
Or M =
∴ M = - 2
So, The slope of other line = M = - 2
<u>Now, equation of line with slope - 2 and points (4 , - 6) in slope-point form</u>
y - = M (x -
)
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