We are given a line passing through the point $(-10, 1)$ and having a slope of $\frac{1}{2}$. To write the equation of the line in slope-intercept form, we can use the point-slope formula:

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

Where:

• $m$ is the slope of the line,
• $(x_1, y_1)$ is a point on the line.

Step 1: Substitute the given values

Using the point $(-10, 1)$ and slope $m = \frac{1}{2}$:

$y - 1 = \frac{1}{2}(x - (-10))$

$y - 1 = \frac{1}{2}(x + 10)$

Step 2: Distribute the slope

Now, distribute $\frac{1}{2}$ on the right-hand side:

$y - 1 = \frac{1}{2}x + 5$

Step 3: Solve for $y$ (get it in slope-intercept form $y = mx + b$)

Add 1 to both sides to isolate $y$:

$y = \frac{1}{2}x + 5 + 1$

$y = \frac{1}{2}x + 6$

Thus, the equation of the line in slope-intercept form is:

$y = \frac{1}{2}x + 6$

Would you like further details on any part of the solution? Here are some related questions:

1. How do you convert from point-slope form to slope-intercept form?
2. What is the significance of the slope in the equation?
3. How do you find the y-intercept from the equation of a line?
4. What is the general form of the equation of a line?
5. How would the equation change if the point or slope were different?

Tip: Remember, the slope of a line describes how steep it is; a slope of $\frac{1}{2}$ means that for every 2 units you move horizontally, the line moves 1 unit vertically.