Question

Write the linear equation -2x+3y=-9 In slope-intercept form

Answer 1

To convert the equation \(-2x + 3y = -9\) into slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

1. Start with the given equation:
\[
-2x + 3y = -9
\]

2. Add \(2x\) to both sides:
\[
3y = 2x - 9
\]

3. Now, divide every term by 3 to isolate \(y\):
\[
y = \frac{2}{3}x - 3
\]

Now the equation is in slope-intercept form. The slope \(m\) is \(\frac{2}{3}\) and the y-intercept \(b\) is \(-3\). Thus, the final equation is:
\[
y = \frac{2}{3}x - 3
\]