Chapter 3.3, Problem 50WE

To determine

To proof:Explain how you know L passes through $P(x_1,y_1)$ .

Answer to Problem 50WE

  $P(x_1,y_1)$ issatisfies the equation of the line L .So , $P(x_1,y_1)$ is on the graph of line Ltherefore is L passes through $P(x_1,y_1)$ .

Explanation of Solution

Given information:Given equation is $y-y_1=m(x-x_1)$ is a line L. equation in the

Calculation:

Let $P(x_1,y_1)$ be a point and m a real number .There is one and only one line L through P having slope m .An equation of L is:

  $y-y_1=m(x-x_1)\mathrm{........}(1)$

When we substitute $x=x_1\text{and}y=y_1$ in equation (1) we see that the equation is satisfied:

  $\begin{array}{c}{y}_1-y_1=m(x_1-x_1).\\ 0=0(\text{TRUE}).\end{array}$

So, $P(x_1,y_1)$ is the solution of the equation (1) therefore point $P(x_1,y_1)$ is on the graph of line L .So, L passes through $P(x_1,y_1)$ .