You can use the fact that perpendicular line segments have their slope as negative reciprocal of slope of each other.
The equation of the line perpendicular to y =m(x+c) with same y intercept is given by:
Option B : [tex]y = -\dfrac{1}{m}(x - m^2c)[/tex]
What is the slope of line which is perpendicular to other line?
The slope of the line which is perpendicular to other line is negative reciprocal of the other line.
Rewriting the equation y = m(x+c) in slope-intercept form, we get:
[tex]y = m(x+c) = mx + mc[/tex]
Thus, slope of this line is m and y -intercept is at y = mc.
Let the line segment perpendicular to this line be y = ax + b
Then its slope 'a' must be negative reciprocal of slope m.
Or
[tex]a = -\dfrac{1}{m}[/tex]
The y intercept is specified to be same
Thus, b = mc
Thus, we have the equation of the line segment which is perpendicular to y = m(x+c) with the same y intercept as:
[tex]y = ax + b\\
y = -\dfrac{1}{m}x + mc\\
\\
y = -\dfrac{1}{m}(x - m^2c)[/tex]
Thus, the equation of the line perpendicular to y =m(x+c) with same y intercept is given by:
Option B : [tex]y = -\dfrac{1}{m}(x - m^2c)[/tex]
Learn more about perpendicular straight lines here:
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