Chapter 8.4, Problem 40E

To determine

To choose:

A point P such that the slope of the line through $(-1,1)$ and P is $\frac{1}{9}$ .

Answer to Problem 40E

The coordinates of point P would be $(8,2)$ .

Explanation of Solution

Given:

A point and slope of line: $(-1,1)$ and $\frac{1}{9}$ .

Calculation:

Let $(x,y)$ represent coordinates of point P .

We will use slope formula to solve our given problem.

  $\text{Slope}=\frac{\text{Rise}}{\text{Run}}$

The numerator of our given fraction represents difference between the y -coordinates and denominator of our given fraction represents difference between the x -coordinates. Using above information, we can set two equations as:

  $\begin{array}{l}x-(-1)=9\\ x+1=9\\ x+1-1=9-1\\ x=8\end{array}$

  $\begin{array}{l}y-1=1\\ y-1+1=1+1\\ y=2\end{array}$

Therefore, the coordinates of point P would be $(8,2)$ .