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To write the equation of the line in slope-intercept form (which is \( y = mx + b \)), we are given:

- A point on the line: \( (-10, 6) \)
- The slope of the line: \( m = -\frac{1}{2} \)

We can use the point-slope formula to find the equation of the line:

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

where \( (x_1, y_1) \) is the point on the line and \( m \) is the slope. Plugging in the values:

\[
y - 6 = -\frac{1}{2}(x + 10)
\]

Now, simplify the equation step by step:

\[
y - 6 = -\frac{1}{2}x - 5
\]

Next, solve for \( y \):

\[
y = -\frac{1}{2}x - 5 + 6
\]
\[
y = -\frac{1}{2}x + 1
\]

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

\[
y = -\frac{1}{2}x + 1
\]

Would you like further explanation on any step, or details on how to solve other forms of line equations?

Here are some related questions to expand your understanding:
1. How can you convert a slope-intercept form equation to standard form?
2. What does the slope tell you about the direction of the line?
3. How would you determine the y-intercept given different points on the line?
4. Can the point-slope formula be used to find equations when the slope is undefined?
5. What happens to the slope-intercept form when the slope is 0?

**Tip:** The slope \( m \) tells you how much the line rises or falls for each unit step along the x-axis.

A line passes through the point (-10, 6) 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 that passes through the point (-10, 6) with a slope of -1/2. This algebra problem involves using point-slope and slope-intercept forms, suitable for students in Grades 8-10.

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