Question

Construct parametric equations describing the graph of the line passing through the following points.(20, -14) and (12, -12)If y = 1-5, find the parametric equation for x,

Answer 1

x = -4t - 16

EXPLANATION :

From the problem, we have the points :

`(20,-14)\quad and\quad(12,-12)`

Solve for the equation of the line using two-point formula :

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

That will be :

`\begin{gathered} y-(-14)=(-12-(-14))/(12-20)(x-20) \\ y+14=(2)/(-8)(x-20) \\ y+14=-(1)/(4)(x-20) \\ y+14=-(1)/(4)x+5 \\ y=-(1)/(4)x+5-14 \\ y=-(1)/(4)x-9 \end{gathered}`

Next is to substitute the given paremetric equation for y :

`y=t-5`

That will be :

`\begin{gathered} y=-(1)/(4)x-9 \\ y=t-5 \\ t-5=-(1)/(4)x-9 \\ t-5+9=-(1)/(4)x \\ t+4=-(1)/(4)x \\ 4t+16=-x \\ x=-4t-16 \end{gathered}`