To find the equation of the line passing through the points $(7, 8)$ and $(-4, 9)$, we'll use the point-slope form of a line, which is given by:

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

Where:

• $m$ is the slope of the line
• $(x_1, y_1)$ is a point on the line

Step 1: Find the slope $m$

The formula to find the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points $(x_1, y_1) = (7, 8)$ and $(x_2, y_2) = (-4, 9)$:

$m = \frac{9 - 8}{-4 - 7} = \frac{1}{-11} = -\frac{1}{11}$

Step 2: Use the point-slope form

Now that we know the slope $m = -\frac{1}{11}$, we can use the point-slope form of the equation with one of the points, say $(7, 8)$:

$y - 8 = -\frac{1}{11}(x - 7)$

Final Answer

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

$y - 8 = -\frac{1}{11}(x - 7)$

If you need any further clarifications or additional steps, feel free to ask!

Additional Questions:

1. How do you convert the point-slope form into slope-intercept form?
2. What happens to the equation if the points have the same $y$-coordinate?
3. How can you determine if two lines are parallel from their equations?
4. What is the formula for the slope when given two points with integer coordinates?
5. How can you identify the slope of a vertical or horizontal line?

Tip:

If the slope $m$ is undefined, the line is vertical, and its equation is of the form $x = c$, where $c$ is the $x$-coordinate of the point.