Chapter 4.3, Problem 54HP

To determine

To find: How slope formula can be used to find the equation of a straight line.

Explanation of Solution

Given information:Considering any two points say $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ through which the line will pass and slope of that line is given by,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Formula used:Equation of line through the point $\left(x_1,y_1\right)$ and slope $m=\frac{y_2-y_1}{x_2-x_1}$ is given by,

  $y-y_1=m\left(x-x_1\right)\mathrm{......}\left(\text{where }m=\frac{y_2-y_1}{x_2-x_1}\right)$

Proof: Since, the given slope of line is $m=\frac{y_2-y_1}{x_2-x_1}$ which passes through the point $\left(x_1,y_1\right)$ . Therefore, the equation of line using point slope form is evaluated as,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\mathrm{......}\left(\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\left(\text{given}\right)\\ \text{and point is }\left(x_1,y_1\right)\end{array}\right)\end{array}$

In this way the equation of straight line of given slope and passing through the given point can be evaluated.