Step 1
State the relationship between the slopes of perpendicular lines
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ \text{where m = slope} \end{gathered}[/tex]The given equation of a line is;
[tex]\begin{gathered} h(t)=-4t+8 \\ \text{From the slope-intercept form of the equation of a line} \\ h(t)=mt+c \\ \text{and comparing both equations} \\ m_1=-4 \end{gathered}[/tex]Step 2
Find m₂
[tex]m_2=-\frac{1}{-4}=\frac{1}{4}[/tex]Step 3
State the equation for a line in the slope-point form and get the equation
[tex]\begin{gathered} g(t)-g(t_1)_{}=m(t-t_1) \\ g(t_1)=-1 \\ m=m_2=\frac{1}{4} \\ t_1=-8 \\ \end{gathered}[/tex][tex]\begin{gathered} g(t)-(-1)=\frac{1}{4}(t-(-8)) \\ g(t)+1=\frac{1}{4}(t+8) \\ g(t)=\frac{1}{4}t+(8)(\frac{1}{4})-1 \\ g(t)=\frac{1}{4}t+2-1 \\ g(t)=\frac{1}{4}t+1 \end{gathered}[/tex]Hence the equation is;
g(t)=(1/4)t+1
