To find the equation of the line passing through the points $(-4, -2)$ and $(4, 0)$, follow these steps:

1. Find the slope ($m$):

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates: $m = \frac{0 - (-2)}{4 - (-4)} = \frac{0 + 2}{4 + 4} = \frac{2}{8} = \frac{1}{4}$

2. Use the point-slope form:

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using one of the points, say $(-4, -2)$, and the slope $m = \frac{1}{4}$: $y - (-2) = \frac{1}{4}(x - (-4))$ Simplify: $y + 2 = \frac{1}{4}(x + 4)$

3. Simplify to slope-intercept form ($y = mx + b$):

Distribute $\frac{1}{4}$: $y + 2 = \frac{1}{4}x + 1$ Subtract 2 from both sides: $y = \frac{1}{4}x - 1$

Final Answer:

The equation of the line is: $y = \frac{1}{4}x - 1$

Would you like a graph or more explanation on how to convert between forms?

Follow-up Questions:

1. How do you find the slope if given two points?
2. What does the slope represent in this equation?
3. How do you convert from point-slope form to slope-intercept form?
4. How can you verify that a point lies on a given line?
5. What is the general form of a linear equation, and how does it relate to this problem?

Tip:

Always double-check your slope calculations by ensuring the numerator and denominator represent the differences in $y$- and $x$-coordinates correctly.