Answer:
[tex]y = -\frac{1}{m}x + mc[/tex]
Explanation:
Given
[tex]y = m(x + c)[/tex]
Required
Determine an equation of a perpendicular line but with the same y intercept
[tex]y = m(x + c)[/tex]
Open bracket
[tex]y = mx + mc[/tex]
A linear equation is represented with:
[tex]y = ax + b[/tex]
Where
[tex]a = slope[/tex]
[tex]b = y\ intercept[/tex]
By comparison:
[tex]a = m[/tex]
[tex]b = mc[/tex]
So, the slope of [tex]y = m(x + c)[/tex] is m
Because the new line is perpendicular to [tex]y = m(x + c)[/tex], the relationship between their slopes is:
[tex]a_2 = -\frac{1}{a_1}[/tex]
Where
[tex]a_1 =[/tex] slope of the first equation
[tex]a_2 =[/tex] slope of the second equation
Substitute m for [tex]a_1[/tex] in [tex]a_2 = -\frac{1}{a_1}[/tex]
[tex]a_2 = -\frac{1}{m}[/tex]
Hence, the slope of the new equation is: [tex]-\frac{1}{m}[/tex]
From the question, we understand that they have the same y intercept.
So, the equation of the new equation is:
[tex]y = -\frac{1}{m}x + mc[/tex]
