To convert the equation 2x + 3y = 6 into slope-intercept form, which is represented as y = mx + b (where m is the slope and b is the y-intercept), we need to isolate y.
Starting with the original equation:
2x + 3y = 6
First, we want to move the term with x to the other side. We can do this by subtracting 2x from both sides:
3y = 6 – 2x
Next, to isolate y, we need to divide every term by 3:
y = rac{6}{3} – rac{2x}{3}
This simplifies to:
y = 2 – rac{2}{3}x
Now we can rearrange it to match the slope-intercept form:
y = - rac{2}{3}x + 2
In this form, we can see that the slope (m) is -2/3 and the y-intercept (b) is 2.