To find the equation of a line passing through two given points, $(-2, -1)$ and $(-4, -3)$, we follow these steps:

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

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

For the points $(-2, -1)$ and $(-4, -3)$: $m = \frac{-3 - (-1)}{-4 - (-2)} = \frac{-3 + 1}{-4 + 2} = \frac{-2}{-2} = 1$

So, the slope $m = 1$.

Step 2: Use the point-slope form of the equation of a line.

The point-slope form is: $y - y_1 = m(x - x_1)$ Using the slope $m = 1$ and one of the points, say $(-2, -1)$: $y - (-1) = 1(x - (-2))$ Simplifying: $y + 1 = 1(x + 2)$ $y + 1 = x + 2$ $y = x + 1$

Final Equation:

The equation of the line is: $y = x + 1$

Would you like more details on this process or have any questions?

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Here are five related questions you might find useful:

1. How do you find the equation of a line given its slope and a point on the line?
2. How do you convert a line equation from point-slope form to slope-intercept form?
3. What are the properties of a line with a slope of 1?
4. How do you calculate the distance between two points on a coordinate plane?
5. How do you write the equation of a line parallel or perpendicular to a given line?

Tip: When calculating the slope, always check for signs carefully to avoid errors.