Chapter 1.1, Problem 39E

To determine

To show: The equation of line is $y=x+1$ if point $\left(3,4\right)$ is used to write the equation.

Explanation of Solution

Given information: The points are $\left(-2,-1\right)$ , and $\left(3,4\right)$ .

Proof:

The formula to find the slope of line passing through two points is given by,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute $-2$ for $x_1$ , $-1$ for $y_1$ , $3$ for $x_2$ , and $4$ for $y_2$ in the above formula.

  $\begin{array}{c}m=\frac{4-\left(-1\right)}{3-\left(-2\right)}\\ =\frac{5}{5}\\ =1\end{array}$

The point slope form of an equation of line is given by,

  $y-y_1=m\left(x-x_1\right)$

Substitute $3$ for $x_1$ , $4$ for $y_1$ , and $1$ for $m$ in the above formula.

  $\begin{array}{c}y-4=1\left(x-3\right)\\ y-4=x-3\\ y=x-3+4\\ y=x+1\end{array}$

Hence, it is shown that the equation of the line is a same as $y=x+1$ .