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

ANSWER :

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 :

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

That will be :

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

Next is to substitute the given paremetric equation for y :

$y=t-5$

That will be :

$\begin{gathered} y=-\frac{1}{4}x-9 \\ y=t-5 \\ t-5=-\frac{1}{4}x-9 \\ t-5+9=-\frac{1}{4}x \\ t+4=-\frac{1}{4}x \\ 4t+16=-x \\ x=-4t-16 \end{gathered}$