https://file.aiquickdraw.com/mathbot/file/1727458961621n3etx6z5.jpg

The tasks in the image involve calculating the slope of a line passing through two given points, writing the equation of the line in point-slope form using the second point, and converting that equation into slope-intercept form.

### a) Calculation of the Slope

Given two points, \((-4, 3)\) and \( (2, -6) \), the formula for the slope \( m \) between these points is:

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

Plugging in the coordinates of the points:

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

### b) Point-Slope Form

Using the second point \((2, -6)\) and the slope \(-\frac{3}{2}\), the point-slope form of the line is given by:

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

Substituting the slope and the second point into the equation:

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

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

### c) Slope-Intercept Form

To convert the point-slope form to slope-intercept form \(y = mx + b\), solve for \(y\):

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

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

This is the equation of the line in slope-intercept form, where the slope \(m = -\frac{3}{2}\) and the y-intercept \(b = -3\).

Would you like further details on any of these calculations, or do you have any additional questions? Here are some related queries:

1. How would you find the x-intercept of this line?
2. What happens if you use the first point in the point-slope form?
3. How can you verify the accuracy of the slope-intercept form?
4. Could you calculate the distance between the two points?
5. What would be the midpoint of the segment joining these two points?

**Tip**: To visually confirm the accuracy of the slope and y-intercept, you could plot the equation on a graph and ensure it passes through the given points.

Given two points (-4, 3) and (2, -6), find the slope, write the equation of the line in point-slope form, and convert it to slope-intercept form.

Learn how to calculate the slope of a line passing through points (-4, 3) and (2, -6). Understand the process of writing the equation in point-slope form and converting it to slope-intercept form. This step-by-step guide is ideal for students in Grades 8-10.

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