https://file.aiquickdraw.com/mathbot/file/172706561315445qn0xjv.jpg

The equation given is:

\[
y = -3x + 2
\]

This is in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

### Solution:
1. **Slope (m)**: The slope is the coefficient of \(x\), which is \(-3\).

2. **y-intercept (b)**: The y-intercept is the constant term, which is \(2\). This means the point where the line crosses the y-axis is \((0, 2)\).

Thus:
- Slope \( = -3 \)
- \( y \)-intercept \( = (0, 2) \)

### Perpendicular Slope:
The slope of a line perpendicular to another is the negative reciprocal of the original slope. The original slope is \(-3\), so the perpendicular slope is:

\[
\text{Perpendicular slope} = \frac{1}{3}
\]

Would you like help sketching the graph or further details on the slope?

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### Related Questions:
1. What is the slope-intercept form of a line with slope 2 and y-intercept \( (0, -4) \)?
2. How do you find the slope of a line from two given points?
3. What is the equation of a line perpendicular to \( y = 5x + 1 \) and passing through the origin?
4. How do you calculate the x-intercept of a line from its equation?
5. How can you determine if two lines are parallel just from their equations?

### Tip:
Always check that your equation is in slope-intercept form (\( y = mx + b \)) before determining the slope and intercepts.

Give the slope and y-intercept for the equation y = -3x + 2, then sketch the graph. Give the slope of any line perpendicular to the given line.

Learn how to find the slope and y-intercept of the equation y = -3x + 2, and calculate the slope of any line perpendicular to it. Suitable for students in Grades 8-10.

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