Question

How do you find the slope given `3y= x -1/2`?

Answer 1

See a solution process below:

Explanation:

First, we can put the equation into slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`3y = x - 1/2`

`(3y)/color(red)(3) = (x - 1/2)/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = x/color(red)(3) - (1/2)/color(red)(3)`

`y = x/3 - 1/6`

`y = color(red)(1/3)x - color(blue)(1/6)`

Therefore, the slope of the line represented by this equation is:

`color(red)(m = 1/3)`