Respuesta :
ANSWER
The slope of the line perpendicular line of the equation is 3
STEP-BY-STEP 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
[tex]y\text{ = mx + b}[/tex]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
[tex]\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} \\ \frac{3y}{3}\text{ = }\frac{-1}{3}x\text{ -}\frac{15}{3} \\ y\text{ = }\frac{-1}{3}x\text{ - 5} \\ \text{Hence, the slope}-\text{intercept form of the above equation is given as} \\ y\text{ = }\frac{-1}{3}x\text{ - 5} \end{gathered}[/tex]NB: That the two lines are perpendicular to each other
From y = mx + b
m = -1/3
The slope of the equation
[tex]\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{ = }\frac{-1}{3} \\ \frac{-1}{3}\cdot m_2\text{ = -1} \\ \frac{-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} \\ \frac{-m_2}{-1}\text{ = }\frac{-3}{-1} \\ m_2\text{ = }3 \\ \text{Hence, the slope of the perpendicular line to the equation is 3} \end{gathered}[/tex]