Question

Construct parametric equations describing the graph of the line passing through the following points.(-1,-16) and (19,11)If x = t - 2, find the parametric equation for y.

Answer 1

The line passes through the point:

`(-1,-16)\text{ and }(19,11)`

We can use the slope-intercept form of a linear equation to get the line:

`y=mx+b`

where

`m=(y_2-y_1)/(x_2-x_1)`

The points are:

`\begin{gathered} (x_1,y_1)=(-1,-16) \\ (x_2,y_2)=(19,11) \end{gathered}`

Using the formula, we have:

`\begin{gathered} m=(11-(-16))/(19-(-1))=(11+16)/(19+1) \\ m=(27)/(20) \end{gathered}`

Thus, the equation is in the form:

`y=(27)/(20)x+b`

At the point (-1, -16), we have:

`\begin{gathered} -16=(27)/(20)(-1)+b \\ -16=-(27)/(20)+b \\ b=-16+(27)/(20) \\ b=-(293)/(20) \end{gathered}`

Therefore, the equation will be:

`y=(27)/(20)x-(293)/(20)`