To determine the equation of the line that passes through the points $(-5, -2)$ and $(5, -8)$, we can follow these steps:

Step 1: Find the slope $m$

The slope formula is:

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

Using the points $(-5, -2)$ and $(5, -8)$:

• $x_1 = -5$, $y_1 = -2$
• $x_2 = 5$, $y_2 = -8$

Substitute into the slope formula:

$m = \frac{-8 - (-2)}{5 - (-5)} = \frac{-8 + 2}{5 + 5} = \frac{-6}{10} = -\frac{3}{5}$

So, the slope of the line is $m = -\frac{3}{5}$.

Step 2: Use the point-slope form to find the equation of the line

The point-slope form of a line is:

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

Using the point $(-5, -2)$ and the slope $m = -\frac{3}{5}$, we substitute:

$y - (-2) = -\frac{3}{5}(x - (-5))$

Simplify:

$y + 2 = -\frac{3}{5}(x + 5)$

Now distribute the slope:

$y + 2 = -\frac{3}{5}x - 3$

Finally, subtract 2 from both sides to get the equation in slope-intercept form:

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

Final Equation of the Line

The equation of the line is:

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

Graphing the Line

To graph the line, plot the two points $(-5, -2)$ and $(5, -8)$ on the coordinate plane, then draw a straight line through them. Since the slope is negative $-\frac{3}{5}$, the line will decrease as you move from left to right.

Do you want to see more details about how to graph this line? Feel free to ask if anything needs clarification!

Here are 5 follow-up questions:

1. How do you calculate the y-intercept from the slope-intercept form of a line?
2. What does the slope of the line indicate about its direction?
3. Can the equation of the line be rewritten in standard form? If so, how?
4. How would the graph of the line change if the slope were positive instead of negative?
5. What are the intercepts of this line on the x-axis and y-axis?

Tip: When graphing, always use at least two points to make sure your line is accurate!