Question

What is the slope-intercept form of the linear equation 2x + 3y = 6?Drag and drop the appropriate number, symbol, or variable to each box.33-61yX1CONmla12/3236+=

Answer 1

A line equation can be written in slope-intercept form, which is

`y=mx+b`

where m represents the slope and b represents the y-intercept.

The line equation on our problem is written in standard form. The given line equation is

`2x+3y=6`

To rewrite in slope intercept form, let's start by subtracting 2x from both sides:

`\begin{gathered} 2x+3y-2x=6-2x \\ 3y=-2x+6 \end{gathered}`

Then, let's multiply both sides by 1/3:

`\begin{gathered} (1)/(3)\cdot3y=(1)/(3)\cdot(-2x+6) \\ y=-(2)/(3)x+2 \end{gathered}`

Thus, this is our equation written in slope-intercept form

`y=-(2)/(3)x+2`