Which of the following represents a line parallel to a line that passes through the points (‒2, ‒4) and (1, 5) and contains the point (1, ‒2)?
A.
X	Y
-2	7
1	-2
4	-11

B.
X	Y
-2	-3
1	-2
4	-1

C.
X	Y
-2	-11
1	-2
4	7

D.
E.

### Step 1: Find the slope of the line that passes through the points (‒2, ‒4) and (1, 5)
The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Here, the points are \((-2, -4)\) and \((1, 5)\), so:

\[
m = \frac{5 - (-4)}{1 - (-2)} = \frac{5 + 4}{1 + 2} = \frac{9}{3} = 3
\]

### Step 2: Determine the equation of the parallel line
Since parallel lines have the same slope, the line parallel to this one must also have a slope of \(3\).

Now, we need to find the equation of the line that has a slope of \(3\) and passes through the point \((1, -2)\). We use the point-slope form of the equation of a line:

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

Substitute \(m = 3\), \(x_1 = 1\), and \(y_1 = -2\):

\[
y - (-2) = 3(x - 1)
\]
\[
y + 2 = 3(x - 1)
\]
\[
y + 2 = 3x - 3
\]
\[
y = 3x - 5
\]

So, the equation of the line is \(y = 3x - 5\).

### Step 3: Check which option contains points on this line
We need to check which of the given options has points that satisfy the equation \(y = 3x - 5\).

**Option A:**

- For \(x = -2\), \(y = 3(-2) - 5 = -6 - 5 = -11\), but option A gives \(y = 7\) (does not match).

**Option B:**

- For \(x = -2\), \(y = 3(-2) - 5 = -6 - 5 = -11\), but option B gives \(y = -3\) (does not match).

**Option C:**

- For \(x = -2\), \(y = 3(-2) - 5 = -6 - 5 = -11\), which matches the value in option C.
- For \(x = 1\), \(y = 3(1) - 5 = 3 - 5 = -2\), which matches.
- For \(x = 4\), \(y = 3(4) - 5 = 12 - 5 = 7\), which matches.

Thus, **Option C** represents the correct line.

---

Would you like more details on how to solve these types of problems?  
Here are five related questions to explore the topic further:

1. How do you find the equation of a line given its slope and a point on the line?
2. What is the difference between parallel and perpendicular lines in terms of their slopes?
3. How can you determine if two lines are parallel from their equations?
4. What is the general form of a linear equation, and how can you convert between forms?
5. How do you find the slope of a line from its graph?

**Tip**: Remember that parallel lines always have the same slope, but different y-intercepts unless they are identical.

Which of the following represents a line parallel to a line that passes through the points (‒2, ‒4) and (1, 5) and contains the point (1, ‒2)?

Solve a problem about finding a line parallel to one passing through points (‒2, ‒4) and (1, 5), with step-by-step instructions on using the slope formula and point-slope form. Explore parallel line properties, suitable for Grades 8-10.

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