Question

Change to slope-intercept form. Then find the y-intercept, first point, and second point.
3y-2x=9
slope intercept form ______
y-intercept _____
first point (let x=0) ____
second point ______

Answer 1

To convert the equation \(3y - 2x = 9\) to slope-intercept form (which is \(y = mx + b\)), we need to solve for \(y\).

Starting with the given equation:

\[ 3y - 2x = 9 \]

1. Add \(2x\) to both sides:

\[ 3y = 2x + 9 \]

2. Now, divide every term by \(3\) to solve for \(y\):

\[ y = \frac{2}{3}x + 3 \]

Now we have the slope-intercept form:

**Slope-Intercept Form:**

\[
y = \frac{2}{3}x + 3
\]

From this equation, we can determine the following:

1. **Slope (m)**: \( \frac{2}{3} \)
2. **y-intercept (b)**: \( 3 \)

**y-intercept:**

The y-intercept is \( (0, 3) \).

**First Point (let \(x=0\)):**

To find the first point, we can simply substitute \(x = 0\) into the equation:

\[
y = \frac{2}{3}(0) + 3 = 3
\]

So, the first point is:

**First Point:** \( (0, 3) \)

**Second Point:**

To find a second point, we can choose another value for \(x\). Let's choose \(x = 3\):

\[
y = \frac{2}{3}(3) + 3 = 2 + 3 = 5
\]

So, the second point is:

**Second Point:** \( (3, 5) \)

**Summary:**

- **Slope-Intercept Form:** \( y = \frac{2}{3}x + 3 \)
- **y-intercept:** \( 3 \)
- **First Point:** \( (0, 3) \)
- **Second Point:** \( (3, 5) \)