Chapter 4.1, Problem 14PPS

To determine

To Find: The equation of the line in slope- intercept form passing through $\left(2,5\right)$ and slope $-2$ .

Answer to Problem 14PPS

The equation of line in slope intercept form is $y=2x+9$ .

Explanation of Solution

Given information:

Line passing through $\left(2,5\right)$ and slope $-2$

Concept and Formula Used:

Equation of line passing through point and given slope $y-y_1=m\left(x-x_1\right)$ . Slope intercept form $y=mx+c$

Calculation:

It is given that line passing through $\left(2,5\right)$ and slope $-2$

Equation of line through point and given slope is

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(2,5\right)\&m=-2\\ y-\left(5\right)=-2\left(x-2\right)\\ y-5=-2x+4\left(\text{Distributive property}\right)\\ \text{Add 5 to both sides}\\ y-5+5=2x+4+5\\ y=2x+9\end{array}$

Conclusion:

The equation of line in slope intercept form is $y=2x+9$ .