Given two points (-4, 3) and (2, -6) find the following:

a) slope = Response area 

b) point slope form (USE THE 2nd POINT) 

y -  = Response area (x - )

c) distribute and combine like terms to write the equation in slope intercept form

y = Response areax + Response area

To solve the problem step by step:

### a) Slope:

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-4, 3)\) and \((2, -6)\):

\[
m = \frac{-6 - 3}{2 - (-4)} = \frac{-6 - 3}{2 + 4} = \frac{-9}{6} = -\frac{3}{2}
\]

**Slope =** \(-\frac{3}{2}\)

### b) Point-slope form (using the 2nd point (2, -6)):

The point-slope form equation is:

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

Using the point \((2, -6)\) and the slope \(m = -\frac{3}{2}\):

\[
y - (-6) = -\frac{3}{2}(x - 2)
\]

Simplified:

\[
y + 6 = -\frac{3}{2}(x - 2)
\]

### c) Distribute and combine like terms to write in slope-intercept form:

Now, let's distribute the \(-\frac{3}{2}\):

\[
y + 6 = -\frac{3}{2}x + 3
\]

Subtract 6 from both sides:

\[
y = -\frac{3}{2}x + 3 - 6
\]

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

### Final Answer:

\[
\text{Slope (a)} = -\frac{3}{2}
\]
\[
\text{Point-Slope Form (b)}: \ y + 6 = -\frac{3}{2}(x - 2)
\]
\[
\text{Slope-Intercept Form (c)}: \ y = -\frac{3}{2}x - 3
\]

Would you like more details or have any questions?

### 5 Related Questions:
1. How do you find the slope when given two points?
2. What is the significance of the slope in a linear equation?
3. How does the point-slope form relate to the slope-intercept form?
4. Can you derive the point-slope form from any point on a line?
5. What are the steps to convert point-slope form to slope-intercept form?

### Tip:
When finding the slope between two points, remember that the change in \(y\) (rise) is divided by the change in \(x\) (run) to calculate it.

Given two points (-4, 3) and (2, -6) find the following: a) slope, b) point slope form (USE THE 2nd POINT), c) distribute and combine like terms to write the equation in slope intercept form.

Learn how to calculate the slope between two points (-4, 3) and (2, -6) and find the equation of the line in both point-slope and slope-intercept forms. This problem involves key algebraic concepts such as slope calculation and equation conversion, suitable for Grades 8-10.

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