Chapter 8.8, Problem 51STP

To determine

To calculate: To write the equation to determine the distance from home at any point during the trip

Answer to Problem 51STP

Theequation to determine the distance of L from home at any point during her trip is $y=65x+320$

Explanation of Solution

Given information: J is $320$ miles from home and is driving home at a speed of $65$ mph.

Formula Used:

Equation of line passing through two points is given as

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

Calculation:

Given that J is $320$ miles from home and is driving home at a speed of $65$ mph.

Let the time be $x$

Let the distance of J from home at any point be $y$

Now, at initial time, distance is $320$ miles

That is, when $x=0$

  $y=320$

Also, given that J is home at a speed of $65$ mph.

Thus,

  $\begin{array}{l}\frac{distance}{time}=Speed\\ \frac{y}{x}=65\\ c=65\end{array}$

Using slope intercept form of line, equation of line is given as

  $y=mx+c$

Substituting the values in above equation,

  $y=65x+320$

Conclusion:

Hence, the required equation is $y=65x+320$