Chapter 4.1, Problem 20PPS

To determine

To Find: The equation of the line in slope- intercept form passing through points $\left(-1,-3\right)\&\left(-2,3\right)$ .

Answer to Problem 20PPS

The equation of line in slope intercept form is $y=-6x-9$ .

Explanation of Solution

Given information:

Line passing through points $\left(-1,-3\right)\&\left(-2,3\right)$

Concept and Formula Used:

Equation of line passing through two points is given by $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$ . Slope intercept form $y=mx+c$

Calculation:

It is given that line passing through points $\left(-1,-3\right)\&\left(-2,3\right)$

Equation of line through two points is

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(-1,-3\right)\&\left(x_2,y_2\right)=\left(-2,3\right)\\ y-\left(-3\right)=\left(\frac{3-\left(-3\right)}{-2-\left(-1\right)}\right)\left(x-\left(-1\right)\right)\\ y+3=\left(\frac{6}{-1}\right)\left(x+1\right)\\ y+3=-6(x+1)\\ y+3=-6x-6\left(\text{Distributive property}\right)\\ \text{Subtract 3 from both sides}\\ y+3-3=-6x-6-3\\ y=-6x-9\end{array}$

Conclusion:

The equation of line in slope intercept form is $y=-6x-9$ .