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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.

Construct parametric equations describing the graph of the line passing through the-example-1
User Hoa Vu
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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)
User Martin Janiczek
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