What is the slope of a line perpendicular to the graph of the equation 5x - 3y =2?

Question

Genesis Allen · Accepted Answer

#-3/5# Given: #5x-3y=2#. First we convert the equation in the form of #y=mx+b#. #:.-3y=2-5x# #y=-2/3+5/3x# #y=5/3x-2/3# The product of the slopes from a pair of perpendicular lines is given by #m_1*m_2=-1#, where #m_1# and #m_2# are the lines' slopes. Here, #m_1=5/3#, and so: #m_2=-1-:5/3# #=-3/5# So, the perpendicular line's slope will be #-3/5#.

Eva Abramson · Answer

The slope of a line perpendicular to the graph of the given equation is #-3/5#.

Given: #5x-3y=2# This is a linear equation in standard form. To determine the slope, convert the equation into slope-intercept form: #y=mx+b#, where #m# is the slope, and #b# is the y-intercept. To convert the standard form to slope-intercept form, solve the standard form for #y#. #5x-3y=2# Subtract #5x# from both sides. #-3y=-5x+2# Divide both sides by #-3#. #y=(-5)/(-3)x-2/3# #y=5/3x-2/3# The slope is #5/3#. The slope of a line perpendicular to the line with slope #5/3# is the negative reciprocal of the given slope, which is #-3/5#. The product of the slope of one line and the slope of a perpendicular line equals #-1#, or #m_1m_2=-1#, where #m_1# is the original slope and #m_2# is the perpendicular slope. #5/3xx(-3/5)=-(15)/(15)=-1# graph{(5x-3y-2)(y+3/5x)=0 [-10, 10, -5, 5]}

Eva Adamson · Answer

undefined To find the slope of a line perpendicular to the graph of the equation $5x - 3y = 2$, first solve for $y$ to put it in slope-intercept form $y = mx + b$. Then, identify the slope of the original line as $m$. The slope of a line perpendicular to it will be the negative reciprocal of $m$.

Given the equation $5x - 3y = 2$, rearrange it to solve for $y$:
$$ 5x - 3y = 2 $$
$$ -3y = -5x + 2 $$
$$ y = \frac{5}{3}x - \frac{2}{3} $$

The slope of the original line is $m = \frac{5}{3}$. The slope of a line perpendicular to it is the negative reciprocal of $m$, which is $-\frac{3}{5}$. Therefore, the slope of a line perpendicular to the graph of $5x - 3y = 2$ is $-\frac{3}{5}$.