Chapter 8, Problem 44SGR

To determine

To write: an equation in point-slope form

Answer to Problem 44SGR

The equation of the line by using point-slope form is: $y-3=-1\left(x-3\right)$

Explanation of Solution

Given:

Consider two points (3,3) and (7,-1).

Formula Used:

The general form of equation of line in point-slope intercept form is calculated as

  $y-y_1=m\left(x-x_1\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Step1: Find slope of the line $\left(m\right)$ by using formula of two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Consider that $\left(x_1,y_1\right)=\left(3,3\right)$ and $\left(x_2,y_2\right)=\left(7,-1\right)$

Put the value in slope formula:

  $\begin{array}{l}m=\frac{-1-3}{7-3}\\ =\frac{-4}{4}\\ =-1\end{array}$

Step2: Put the value of $\left(x_1,y_1\right)=\left(3,3\right)$ and $m=-1$ in formula.

  $y-3=-1\left(x-3\right)$

Conclusion:

Therefore, the equation of the line by using point-slope form is: $y-3=-1\left(x-3\right)$ .