Question

What is the slope of the line whose equation is 2x-3y=5

Answer 1

`\large\boxed{\text{The slope}\ m=(2)/(3)}`

Explanation:

The slope-intercept form of a line:

`y=mx+b`

m - slope

b - y-intercept

We have the standard form of a line:

`2x-3y=5`

Convert to the slope-intercept form:

`2x-3y=5` subtract 2x from both sides

`-3y=-2x+5` divide both sides by (-3)

`y=(-2)/(-3)x+(5)/(-3)\\\\y=(2)/(3)x=-(5)/(3)\to m=(2)/(3)`

Answer 2

Explanation:

subtract 2x from both sides of the equation

-3y=-2x+5

Divide each by -3 and simplify

- 3y/-3=-2x/-3+5/-3

reduce and cancel the common numbers

move the negative over from the denominator

-(-1*y)= - 2x/-3 +5/-3

simplify

- -2x/3

multiply 2x/3 by 1

y=2x/3+5/-3

move the negative in front of fraction

y=2x/3 -5/3

slope intercept form

y=2/3 x -5/3

the slope is 2/3