Write the equation of the line that passes through the points left parenthesis, minus, 3, comma, minus, 5, right parenthesis(−3,−5) and left parenthesis, minus, 2, comma, minus, 4, right parenthesis(−2,−4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through the points \((-3, -5)\) and \((-2, -4)\), we'll use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is a point on the line, and \(m\) is the slope of the line.

### Step 1: Calculate the slope (\(m\))
The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the coordinates of the points \((-3, -5)\) and \((-2, -4)\):

\[
m = \frac{-4 - (-5)}{-2 - (-3)} = \frac{-4 + 5}{-2 + 3} = \frac{1}{1} = 1
\]

### Step 2: Use the point-slope form
Now that we have the slope \(m = 1\), we can use one of the points, say \((-3, -5)\), to write the equation of the line:

\[
y - (-5) = 1(x - (-3))
\]

Simplifying:

\[
y + 5 = 1(x + 3)
\]

This is the point-slope form of the equation. To fully simplify it:

\[
y + 5 = x + 3
\]

Finally, subtract 5 from both sides:

\[
y = x - 2
\]

### Final Answer:
The equation of the line in fully simplified form is:

\[
y = x - 2
\]

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How do you convert the equation of a line from point-slope form to slope-intercept form?
2. What is the general formula for finding the distance between two points?
3. How can you determine if two lines are parallel or perpendicular?
4. What is the significance of the slope in the equation of a line?
5. How can you find the y-intercept of a line given two points?

**Tip:** Always check the slope calculation carefully to ensure accuracy when forming the equation of a line.

Learn how to find the equation of a line passing through the points (-3, -5) and (-2, -4) using the point-slope form. This problem covers coordinate geometry concepts, including calculating slope and using point-slope form to derive the equation of a line. Suitable for students in Grades 7-9.

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