find point slope for from 3x+2y=2 with point (4,-2) given

To find the point-slope form of a line, we use the formula:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( (x_1, y_1) \) is the given point, in this case \( (4, -2) \),
- \( m \) is the slope of the line.

### Step 1: Rewrite the equation in slope-intercept form to find the slope.
Given equation: 

\[
3x + 2y = 2
\]

Solve for \( y \):

\[
2y = -3x + 2
\]

\[
y = -\frac{3}{2}x + 1
\]

So the slope \( m = -\frac{3}{2} \).

### Step 2: Apply the point-slope formula.
Using the point \( (4, -2) \) and the slope \( m = -\frac{3}{2} \), we plug into the point-slope formula:

\[
y - (-2) = -\frac{3}{2}(x - 4)
\]

Simplify:

\[
y + 2 = -\frac{3}{2}(x - 4)
\]

This is the point-slope form of the equation.

Would you like more details on any step?

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**Related Questions:**
1. How do you convert from point-slope form to slope-intercept form?
2. How can you graph a line using the point-slope form?
3. What is the meaning of the slope and how can it be interpreted geometrically?
4. How do you find the equation of a line given two points?
5. What is the significance of the point-slope form compared to other forms of linear equations?

**Tip:** Always double-check if the point you are using satisfies the original equation to avoid calculation errors!

Find point-slope form from 3x + 2y = 2 with point (4, -2) given.

Learn how to find the point-slope form of the line 3x + 2y = 2 passing through the point (4, -2). This problem explains the steps for rewriting the equation in slope-intercept form to find the slope and then applying the point-slope formula. Suitable for students in Grades 8-10.

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