Chapter 4.2, Problem 45HP

To determine

To Find: The equation of the line in point slope form passing through points $\left(f,g\right)\&\left(h,j\right)$ .

Answer to Problem 45HP

The equation of line in point slope form is $y-g=\left(\frac{j-g}{h-f}\right)\left(x-f\right)$

Explanation of Solution

Given information:

Line passing through points $\left(f,g\right)\&\left(h,j\right)$

Concept and Formula Used:

Equation of in point slope form is given by $y-y_1=m\left(x-x_1\right)$ where $m=\left(\frac{y_2-y_1}{x_2-x_1}\right)$

Calculation:

It is given that line passing through points $\left(f,g\right)\&\left(h,j\right)$

Slope of line is

  $\begin{array}{l}m=\left(\frac{y_2-y_1}{x_2-x_1}\right)\\ \text{where }\left(x_1,y_1\right)=\left(f,g\right)\&\left(x_2,y_2\right)=\left(h,j\right)\\ m=\left(\frac{j-g}{h-f}\right)\end{array}$

The equation of line in point slope form is

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(f,g\right)\&m=\left(\frac{j-g}{h-f}\right)\\ y-g=\left(\frac{j-g}{h-f}\right)\left(x-f\right)\end{array}$

Conclusion:

The equation of line in point slope form is $y-g=\left(\frac{j-g}{h-f}\right)\left(x-f\right)$