132k views
4 votes
What is the slope of a line perpendicular to the line whose equation is x+3y=-15. Fully simplify your answer.

User Melvio
by
8.2k points

1 Answer

4 votes

ANSWER

The slope of the line perpendicular line of the equation is 3

Explanation:

What to find? The slope of a line perpendicular to the line whose equation is x + 3y = -15

Given the equation

x + 3y = -15

The slope-intercept form of an equation is given as


y\text{ = mx + b}

Where m = slope of the line

y = the intercept of the y-axis

The next step is to re-arrange the above equation in the slope-intercept format


\begin{gathered} \text{Given the equation of a straight line as} \\ x\text{ + 3y = -15} \\ \text{Isolate 3y by substracting x from both sides} \\ x\text{ - x + 3y = -15 - x} \\ 3y\text{ = -x - 15} \\ \text{Divide through by 3} \\ (3y)/(3)\text{ = }(-1)/(3)x\text{ -}(15)/(3) \\ y\text{ = }(-1)/(3)x\text{ - 5} \\ \text{Hence, the slope}-\text{intercept form of the above equation is given as} \\ y\text{ = }(-1)/(3)x\text{ - 5} \end{gathered}

NB: That the two lines are perpendicular to each other

From y = mx + b

m = -1/3

The slope of the equation


\begin{gathered} \text{ For two perpendicular lines, we can calculate the slope as follows} \\ m_1\cdot m_2\text{ =- 1} \\ \text{where m}_1\text{ = }(-1)/(3) \\ (-1)/(3)\cdot m_2\text{ = -1} \\ (-1\cdot m_2)/(3)=\text{ -1} \\ \text{Cross multiply} \\ -m_2\text{ = -1 }\cdot\text{ 3} \\ -m_2\text{ = -3} \\ \text{Divide through by -1} \\ (-m_2)/(-1)\text{ = }(-3)/(-1) \\ m_2\text{ = }3 \\ \text{Hence, the slope of the perpendicular line to the equation is 3} \end{gathered}

User Obimod
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories