Question

Write an equation for a line g(t) perpendicular to h(t) = -4t + 8 and passing through the point (-8, -1).g(t) =

Answer 1

Step 1

State the relationship between the slopes of perpendicular lines

`\begin{gathered} m_2=-(1)/(m_1) \\ \text{where m = slope} \end{gathered}`

The given equation of a line is;

`\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}`

Step 2

Find m₂

`m_2=-(1)/(-4)=(1)/(4)`

Step 3

State the equation for a line in the slope-point form and get the equation

`\begin{gathered} g(t)-g(t_1)_{}=m(t-t_1) \\ g(t_1)=-1 \\ m=m_2=(1)/(4) \\ t_1=-8 \\ \end{gathered}`

`\begin{gathered} g(t)-(-1)=(1)/(4)(t-(-8)) \\ g(t)+1=(1)/(4)(t+8) \\ g(t)=(1)/(4)t+(8)((1)/(4))-1 \\ g(t)=(1)/(4)t+2-1 \\ g(t)=(1)/(4)t+1 \end{gathered}`

Hence the equation is;

g(t)=(1/4)t+1