What is the equation of the line that passes through the point (−8,4) and has a slope of −1/2

To find the equation of the line that passes through the point \((-8, 4)\) and has a slope of \(-\frac{1}{2}\), we use the **point-slope form** of the equation of a line:

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

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

Substituting the values:
- \(m = -\frac{1}{2}\),
- \(x_1 = -8\),
- \(y_1 = 4\),

\[
y - 4 = -\frac{1}{2}(x + 8)
\]

Now, simplify:

\[
y - 4 = -\frac{1}{2}x - 4
\]

Add 4 to both sides to isolate \(y\):

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

Thus, the equation of the line is:

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

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the point-slope form of a line equation used for?
2. How would the equation change if the slope was positive \(\frac{1}{2}\)?
3. Can you convert this equation to standard form \(Ax + By = C\)?
4. How do you graph a line using a point and its slope?
5. What is the slope-intercept form of a line equation?

**Tip:** The slope tells you how steep the line is and its direction; a negative slope indicates the line falls as it moves from left to right.

What is the equation of the line that passes through the point (−8,4) and has a slope of −1/2?

Learn how to find the equation of a line passing through the point (−8, 4) with a slope of −1/2. This solution explains the use of point-slope form and how to simplify it to slope-intercept form, ideal for students in Grades 8-10.

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