Question

What is the slope of the line with the following equation? 1" title="2x+3y=2" alt="2x+3y=2" align="absmiddle" class="latex-formula">

Answer 1

Answer:

slope = - $\frac{2}{3}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 3y = 2 into this form

Subtract 2x from both sides

3y = - 2x + 2 ( divide all terms by 3 )

y = - $\frac{2}{3}$ x + $\frac{2}{3}$ ← in slope- intercept form

with slope m = - $\frac{2}{3}$

Answer 2

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.

$2x+3y=2 \rightarrow 3y=2-2x\ or\ 3y=-2x-2$

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.

$\frac{3y}{3}=\frac{-2x-2}{3} \\ \\ y=-\frac{2}{3}x-\frac{2}{3}$

Now the equation has been changed to slope-intercept form. In the equation, m has been replaced by $-\frac{2}{3}$, which means that is your answer.

Answer: $-\frac{2}{3}$