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

2 Answers
May 27, 2018

Answer:

#-3/5#

Explanation:

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#.

May 27, 2018

Answer:

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

Explanation:

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]}