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!