Use the given conditions to write an equation for the line in​ point-slope form and in​ slope-intercept form.
Slope​ = negative one half
​, passing through left parenthesis 2 comma negative 8 right parenthesis

We are given the following information:

- Slope \( m = -\frac{1}{2} \)
- A point \( (2, -8) \) that the line passes through.

### 1. **Point-Slope Form:**

The point-slope form of a line is given by the formula:

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

Where:
- \( m \) is the slope,
- \( (x_1, y_1) \) is the point the line passes through.

Substituting \( m = -\frac{1}{2} \), \( x_1 = 2 \), and \( y_1 = -8 \) into the equation:

\[
y - (-8) = -\frac{1}{2}(x - 2)
\]

Simplifying:

\[
y + 8 = -\frac{1}{2}(x - 2)
\]

This is the **point-slope form** of the equation.

### 2. **Slope-Intercept Form:**

The slope-intercept form of a line is:

\[
y = mx + b
\]

We know \( m = -\frac{1}{2} \), and we can find the y-intercept \( b \) by using the point \( (2, -8) \). Substitute these values into the slope-intercept equation:

\[
-8 = -\frac{1}{2}(2) + b
\]

Simplify:

\[
-8 = -1 + b
\]

Solving for \( b \):

\[
b = -8 + 1 = -7
\]

Thus, the **slope-intercept form** of the equation is:

\[
y = -\frac{1}{2}x - 7
\]

### Summary:
- **Point-Slope Form**: \( y + 8 = -\frac{1}{2}(x - 2) \)
- **Slope-Intercept Form**: \( y = -\frac{1}{2}x - 7 \)

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How do you convert point-slope form to slope-intercept form?
2. Can you derive the equation of a line given two points instead of slope and one point?
3. How does the slope of a line affect its graphical representation?
4. What is the general method for finding the slope between two points?
5. How do parallel and perpendicular lines relate in terms of slope?

**Tip:** When you know the slope and a point on a line, point-slope form is the easiest starting point to find the equation.

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Slope = negative one half, passing through (2, -8).

Learn how to write the equation of a line given a slope of -1/2 and a point (2, -8) using point-slope and slope-intercept forms. This step-by-step solution explains key concepts in algebra and is ideal for students in Grades 8-10.

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