Chapter 4.2, Problem 49PFA

To determine

To Find: The equation of the line passing through points $\left(2,4\right)\&\left(-3,-6\right)$ .

Answer to Problem 49PFA

The equation of line is $y-4=2\left(x-2\right)$ option ‘A’ is correct.

Explanation of Solution

Given information:

Line passing through points $\left(2,4\right)\&\left(-3,-6\right)$

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 $\left(2,4\right)\&\left(-3,-6\right)$

Slope of line is

  $\begin{array}{l}m=\left(\frac{y_2-y_1}{x_2-x_1}\right)\\ \text{where }\left(x_1,y_1\right)=\left(2,4\right)\&\left(x_2,y_2\right)=\left(-3,-6\right)\\ m=\left(\frac{-6-4}{-3-2}\right)=\frac{-10}{-5}\\ m=2\end{array}$

The equation of line in point slope form is

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(2,4\right)\&m=2\\ y-4=2\left(x-2\right)\end{array}$

Conclusion:

The equation of line is $y-4=2\left(x-2\right)$ option ‘A’ is correct.