To find the equation of a line given two points $(-5, 0)$ and $(5, -4)$, we need to follow these steps:

Step 1: Calculate the slope $m$ of the line.

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points $(-5, 0)$ and $(5, -4)$: $m = \frac{-4 - 0}{5 - (-5)} = \frac{-4}{5 + 5} = \frac{-4}{10} = -\frac{2}{5}$

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

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using the point $(-5, 0)$ and the slope $m = -\frac{2}{5}$, we get: $y - 0 = -\frac{2}{5}(x - (-5))$ Simplifying this: $y = -\frac{2}{5}(x + 5)$

Step 3: Expand and simplify.

Expand the equation: $y = -\frac{2}{5}x - \frac{2}{5} \times 5$ $y = -\frac{2}{5}x - 2$

Thus, the equation of the line is: $y = -\frac{2}{5}x - 2$

Would you like more details or have any questions?

Here are 5 related questions to practice:

1. What is the slope of the line that passes through the points $(2, 3)$ and $(6, -1)$?
2. How do you convert a line equation from point-slope form to slope-intercept form?
3. Can you write the equation of a line parallel to $y = \frac{3}{4}x + 2$?
4. What is the equation of a line perpendicular to $y = -2x + 1$ that passes through the point $(4, -3)$?
5. How do you find the x- and y-intercepts of the line $2x - 3y = 6$?

Tip: When writing the equation of a line, always start by calculating the slope before moving to the equation forms.