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To write the equation of a line in both point-slope form and slope-intercept form, given two points, you can follow these steps:

### 1. Calculate the Slope
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given points \((-3, -4)\) and \((2, 6)\):
\[
m = \frac{6 - (-4)}{2 - (-3)} = \frac{10}{5} = 2
\]

### 2. Point-Slope Form
The point-slope form of a line equation is:
\[
y - y_1 = m(x - x_1)
\]
Using point \((-3, -4)\) and slope \(2\):
\[
y - (-4) = 2(x - (-3))
\]
Simplifying, we get:
\[
y + 4 = 2(x + 3)
\]
\[
y + 4 = 2x + 6
\]
\[
y = 2x + 2
\]

### 3. Slope-Intercept Form
The equation \(y = 2x + 2\) is already in the slope-intercept form, where \(y = mx + b\) and \(b\) is the y-intercept.

Therefore, the equations of the line in both forms are:
- **Point-Slope Form:** \(y + 4 = 2(x + 3)\)
- **Slope-Intercept Form:** \(y = 2x + 2\)

Would you like more details on this process or have any other questions? Here are some related topics you might find interesting:

1. How do you determine the x- and y-intercepts from the slope-intercept form of a line?
2. What changes in the equation of the line if it passes through different points?
3. How do you convert an equation from point-slope form to standard form?
4. How can you determine if two points will create a vertical or horizontal line?
5. What are the implications of a zero or undefined slope?

**Tip:** When solving for the line's equation through two points, always verify your calculations by substituting the coordinates of both points into the final equation to ensure they satisfy it.

Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through (-3, -4) and (2, 6).

Learn how to find the equation of a line passing through the points (-3, -4) and (2, 6) in both point-slope and slope-intercept form. This problem covers essential algebraic concepts such as slope, point-slope form, and slope-intercept form, suitable for students in Grades 8-10.

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