Question

convert and write the equation in slope intercept form. y+3=-2/3(x-3)

Answer 1

To convert the equation \( y + 3 = -\frac{2}{3}(x - 3) \) into slope-intercept form (which is \( y = mx + b \)), follow these steps:

1. Distribute \(-\frac{2}{3}\) on the right side:
\[
y + 3 = -\frac{2}{3}x + \frac{2}{3} \cdot 3
\]

2. Simplify the right side:
\[
\frac{2}{3} \cdot 3 = 2
\]
So, the equation becomes:
\[
y + 3 = -\frac{2}{3}x + 2
\]

3. Now, isolate \(y\) by subtracting 3 from both sides:
\[
y = -\frac{2}{3}x + 2 - 3
\]

4. Combine the constants:
\[
2 - 3 = -1
\]
Therefore:
\[
y = -\frac{2}{3}x - 1
\]

The equation in slope-intercept form is:
\[
\boxed{y = -\frac{2}{3}x - 1}
\]