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The problem is asking for the equation of a line passing through two points: (-4, -7) and (2, 5). To find the equation of the line, we can use the slope-intercept form:

\[
y = mx + b
\]

Where \(m\) is the slope, and \(b\) is the y-intercept. Here's how we can find the slope and the full equation:

### Step 1: Find the slope \(m\)
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points \((-4, -7)\) and \((2, 5)\):

\[
m = \frac{5 - (-7)}{2 - (-4)} = \frac{5 + 7}{2 + 4} = \frac{12}{6} = 2
\]

### Step 2: Use the slope-point form to find the equation
Now that we know the slope is 2, we use the slope-point form:

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

We can use either point. Let's use the point \((2, 5)\):

\[
y - 5 = 2(x - 2)
\]

Simplifying this equation:

\[
y - 5 = 2x - 4
\]

\[
y = 2x - 4 + 5
\]

\[
y = 2x + 1
\]

### Final Answer:
The equation of the line is:

\[
y = 2x + 1
\]

Would you like more details on any of these steps, or have further questions?

### Related Questions:
1. How can you convert a line equation from point-slope form to slope-intercept form?
2. What is the general form of a linear equation, and how does it differ from slope-intercept form?
3. How do you find the equation of a line parallel to a given line?
4. What is the importance of the y-intercept in a linear equation?
5. How do you determine the slope of a vertical or horizontal line?

### Tip:
Always double-check the slope calculation when given two points, as an error there will affect the entire equation!

Find the equation (in terms of x) of the line through the points (-4,-7) and (2,5).

Learn how to find the equation of a line that passes through the points (-4, -7) and (2, 5) using slope and intercept formulas. Suitable for Grades 8-10 students exploring linear functions and algebra.

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