Answer:
[tex]k=-\frac{1}{4}[/tex]
Step-by-step explanation:
we have
Line 1
[tex]y=4x+1[/tex]
Equation in slope intercept form
The slope is equal to
[tex]m_1=4[/tex]
Line 2
[tex]y-kx=10[/tex]
[tex]y=kx+10[/tex]
Equation in slope intercept form
The slope is equal to
[tex]m_2=k[/tex]
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)
so
[tex]m_1*m_2=-1[/tex]
substitute
[tex](4)(k)=-1[/tex]
[tex]k=-\frac{1}{4}[/tex]
