To find the equation of the line in slope-intercept form ($y = mx + b$), we need to determine the slope $m$ and the y-intercept $b$. Given the points $(-6, 1)$ and $(6, -9)$, follow these steps:

1. Find the slope $m$:

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 $(-6, 1)$ and $(6, -9)$:

$m = \frac{-9 - 1}{6 - (-6)} = \frac{-10}{6 + 6} = \frac{-10}{12} = \frac{-5}{6}$

2. Find the equation using point-slope form:

The point-slope form of a line is:

$y - y_1 = m(x - x_1)$

Using $(-6, 1)$ as $(x_1, y_1)$ and the slope $m = \frac{-5}{6}$:

$y - 1 = \frac{-5}{6}(x + 6)$

3. Simplify to slope-intercept form:

Distribute $\frac{-5}{6}$ on the right-hand side:

$y - 1 = \frac{-5}{6}x - 5$

Now, add 1 to both sides:

$y = \frac{-5}{6}x - 4$

Thus, the equation of the line in slope-intercept form is:

$y = \frac{-5}{6}x - 4$

Would you like more details or have any questions?

5 Related Questions:

1. How do you calculate the slope when given two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you find the y-intercept once the slope is known?
4. Can you determine the slope-intercept form from just one point?
5. How does a negative slope affect the direction of a line?

Tip:

Always double-check the signs when calculating the slope from two points, especially when dealing with negative values.