Question

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

Answer 1

`-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`.

Answer 2

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]}