Question

Change to slope-intercept form. Then find the y-intercept, first point, and second point.
-x+3y>6
slope intercept form ______
y-intercept _____
first point (let x=0) ____
second point ______

Answer 1

To convert the inequality \(-x + 3y > 6\) to slope-intercept form (which is \(y = mx + b\)), we start by isolating \(y\).

1. Start with the original inequality:
\[
-x + 3y > 6
\]

2. Add \(x\) to both sides:
\[
3y > x + 6
\]

3. Divide every term by \(3\) to solve for \(y\):
\[
y > \frac{1}{3}x + 2
\]

Now, the slope-intercept form is:
\[
y = \frac{1}{3}x + 2
\]
(Note: We typically write the inequality as \(y <\) or \(y >\) depending on the original inequality, but since you asked for slope-intercept, we'll express only the equality part.)

### Now let's find the requested values:

**Slope-Intercept Form:**
\[
y = \frac{1}{3}x + 2
\]

**y-Intercept:**
The y-intercept occurs when \(x = 0\):
\[
y = \frac{1}{3}(0) + 2 = 2
\]

So, the y-intercept is:
\[
(0, 2)
\]

**First Point (let \(x = 0\)):**
Using \(x = 0\):
\[
y = \frac{1}{3}(0) + 2 = 2
\]

First point is:
\[
(0, 2)
\]

**Second Point (choose another \(x\) value):**
Let’s choose \(x = 3\):
\[
y = \frac{1}{3}(3) + 2 = 1 + 2 = 3
\]

So, another point is:
\[
(3, 3)
\]

### Summary:
- Slope-Intercept Form: \(y = \frac{1}{3}x + 2\)
- Y-Intercept: \( (0, 2) \)
- First Point: \( (0, 2) \)
- Second Point: \( (3, 3) \)