We are given two points $(0, -8)$ and $(5, -5)$ and need to determine the equation of the line passing through them.

Step 1: Find the slope ($m$)

The slope formula is:

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

Substitute $(x_1, y_1) = (0, -8)$ and $(x_2, y_2) = (5, -5)$:

$m = \frac{-5 - (-8)}{5 - 0} = \frac{-5 + 8}{5} = \frac{3}{5}$

So, the slope $m = \frac{3}{5}$.

Step 2: Use the point-slope form

The point-slope form of the equation of a line is:

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

Substituting $m = \frac{3}{5}$ and the point $(0, -8)$:

$y - (-8) = \frac{3}{5}(x - 0)$

Simplifying:

$y + 8 = \frac{3}{5}x$

Now, subtract 8 from both sides:

$y = \frac{3}{5}x - 8$

Thus, the equation of the line is:

$y = \frac{3}{5}x - 8$

Step 3: Graph the line

• The line passes through the points $(0, -8)$ and $(5, -5)$.
• The slope $m = \frac{3}{5}$ means that for every 5 units to the right, the line goes up 3 units.
• The y-intercept is $-8$, meaning the line crosses the y-axis at $(0, -8)$.

Would you like a more detailed explanation or graphing assistance?

Here are some related questions for practice:

1. How do you find the slope if given two points?
2. What is the point-slope form of a linear equation?
3. How can you identify the y-intercept from an equation?
4. How does the slope affect the direction of a line on a graph?
5. Can you find the equation of a line perpendicular to this one?

Tip: Always check that your line passes through both points by substituting them back into the equation.