The question asks for the equation of the line passing through the points $(-4, 1)$ and $(10, 10)$. Here's the solution:

Step 1: Find the slope (m)

The formula for the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute $(x_1, y_1) = (-4, 1)$ and $(x_2, y_2) = (10, 10)$:

$m = \frac{10 - 1}{10 - (-4)} = \frac{9}{14}$

So, the slope $m = \frac{9}{14}$.

Step 2: Use the point-slope form

The point-slope form of a line is:

$y - y_1 = m(x - x_1)$

Substitute $m = \frac{9}{14}$, and use the point $(-4, 1)$:

$y - 1 = \frac{9}{14}(x - (-4))$

Simplify:

$y - 1 = \frac{9}{14}(x + 4)$

$y - 1 = \frac{9}{14}x + \frac{36}{14}$

$y - 1 = \frac{9}{14}x + \frac{18}{7}$

Add $1$ to both sides:

$y = \frac{9}{14}x + \frac{18}{7} + 1$

Convert $1$ to a fraction with denominator 7:

$y = \frac{9}{14}x + \frac{18}{7} + \frac{7}{7}$

$y = \frac{9}{14}x + \frac{25}{7}$

Final Equation

The equation of the line is:

$y = \frac{9}{14}x + \frac{25}{7}$

Would you like further details or have any questions? 😊
Here are 5 related questions for further exploration:

1. How do you find the slope if the two points are vertically aligned?
2. How do you convert the equation to standard form $Ax + By = C$?
3. What is the y-intercept of the line, and how is it calculated?
4. How can you verify if another point lies on this line?
5. How do you find the equation of a line parallel to this one?

Tip: Always check your slope calculation carefully, as small sign errors can lead to incorrect results.