 Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)

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.

Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)?

Learn how to find the equation of a line passing through the points (-2, -1) and (-4, -3) with a detailed step-by-step solution. This problem covers slope calculations and point-slope form, making it suitable for Grades 8-10.

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