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.