QUESTION
Your equation is 2x+3y=2 and you need to find the slope.
EXPLANATION
There are many ways to find the slope with an equation like this. I'm going to change the equation into slope-intercept form.
Slope-intercept form is formatted like this:
y=mx+b
m represents the slope. The first thing you need to do is leave 3y alone to change the equation into slope-intercept form. That means you need to subtract 2x from both sides.
[tex]2x+3y=2 \rightarrow 3y=2-2x\ or\ 3y=-2x-2[/tex]
The next thing you need to do is leave y alone, just like the slope-intercept form example. To leave y alone, you need to divide 3y by 3.
[tex]\frac{3y}{3}=\frac{-2x-2}{3} \\ \\ y=-\frac{2}{3}x-\frac{2}{3}[/tex]
Now the equation has been changed to slope-intercept form. In the equation, m has been replaced by [tex]-\frac{2}{3}[/tex], which means that is your answer.
Answer: [tex]-\frac{2}{3}[/tex]
