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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.

A line passes through the point (-10, 1) and has a slope of 1/2. Write an equation in slope-intercept form for this line.

Learn how to find the equation of a line passing through the point (-10, 1) with a slope of 1/2. This problem involves using the point-slope form and converting it to slope-intercept form. Suitable for students in Grades 8-10.

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