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We are asked to find the slope-intercept equation of a line given that it passes through the point (-6, 8) and is perpendicular to a line with an x-intercept of 2 and a y-intercept of -4.

### Step 1: Find the slope of the given line
We know the line has an x-intercept of 2 and a y-intercept of -4. The slope of this line can be found using the formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, the points are \((2, 0)\) (x-intercept) and \((0, -4)\) (y-intercept):
\[
m = \frac{0 - (-4)}{2 - 0} = \frac{4}{2} = 2
\]
So, the slope of the given line is 2.

### Step 2: Find the slope of the perpendicular line
Since the lines are perpendicular, their slopes are negative reciprocals of each other. If the slope of one line is \(2\), the slope \(m_{\perp}\) of the perpendicular line is:
\[
m_{\perp} = -\frac{1}{2}
\]

### Step 3: Use point-slope form to find the equation of the line
We know the slope of the line we are interested in is \(-\frac{1}{2}\) and it passes through the point \((-6, 8)\). Using the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
Substitute \(m = -\frac{1}{2}\), \(x_1 = -6\), and \(y_1 = 8\):
\[
y - 8 = -\frac{1}{2}(x - (-6))
\]
Simplify:
\[
y - 8 = -\frac{1}{2}(x + 6)
\]
\[
y - 8 = -\frac{1}{2}x - 3
\]
Add 8 to both sides:
\[
y = -\frac{1}{2}x + 5
\]

### Final Equation
The slope-intercept form of the equation is:
\[
y = -\frac{1}{2}x + 5
\]

Do you want further details or have any questions?

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Here are 5 follow-up questions:
1. How do you find the slope between two points on a line?
2. What is the relationship between slopes of perpendicular lines?
3. How does the point-slope form of a line differ from slope-intercept form?
4. Can you derive the equation of a line given only two points?
5. How do x- and y-intercepts help determine the equation of a line?

**Tip**: Always check the relationship between the slopes of perpendicular lines—they are negative reciprocals.

Write the slope-intercept equation of the function f whose graph passes through (-6, 8) and is perpendicular to the line with an x-intercept of 2 and a y-intercept of -4.

Learn how to find the slope-intercept equation of a line passing through the point (-6, 8) and perpendicular to a line with intercepts at x = 2 and y = -4. This algebra problem involves using slope formulas and understanding perpendicular lines.

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