How do you find the slope that is perpendicular to the line #3x-5y=-8#?

Question

Hazel Anglin · Accepted Answer

See a solution process below:

This equation is in Standard Form for a Linear Equation. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)# Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1 #color(red)(3)x - color(blue)(5)y = color(green)(-8)# The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)# Substituting and calculating #m# gives: #m = color(red)(-3)/color(blue)(-5) = 3/5# Let's call the slope of the perpendicular line: #m_p# The formula to find the slope of a perpendicular line is: #m_p = -1/m# Substituting the slope we calculated above gives: #m_p = -1/(3/5)# #m_p = -5/3#

Kennedy Adams · Answer

undefined To find the slope that is perpendicular to the line 3x - 5y = -8, first rearrange the equation into slope-intercept form (y = mx + b), where m is the slope. To do this, solve for y to get y = (3/5)x + 8/5. The perpendicular slope will be the negative reciprocal of 3/5. So, flip the fraction and change its sign, which gives -5/3. Therefore, the slope that is perpendicular to the line 3x - 5y = -8 is -5/3.