Answer:
The slope of the perpendicular line is [tex]-\frac{6}{5}[/tex]
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- The product of the slopes of the perpendicular lines is -1. which means if the slope of one of them is m, then the slope of the other is [tex]-\frac{1}{m}[/tex]
∵ The equation of the given line is 10x - 12y = -24
→ We need to form this equation as the form above to find m
→ Subtract 10x from both sides
∵ 10x - 10x - 12y = -24 - 10x
∴ - 12y = -24 - 10x
→ Divide both sides by -12
∴ [tex]\frac{-12y}{-12}=\frac{-24}{-12}-\frac{10}{-12} x[/tex]
∴ y = 2 - ([tex]\frac{-5}{6}[/tex]) x
→ Remember that (-)(-) = (+)
∴ y = 2 + [tex]\frac{5}{6}[/tex] x
∵ y = m x + b
∴ m = [tex]\frac{5}{6}[/tex]
∴ The slope of the given line is [tex]\frac{5}{6}[/tex]
→ To find the slope of the perpendicular line reciprocal it and change
its sign
∵ The reciprocal of [tex]\frac{5}{6}[/tex] is [tex]\frac{6}{5}[/tex]
→ Change its sign from + to -
∴ The slope of the perpendicular line is [tex]-\frac{6}{5}[/tex]
