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To solve this problem, we need to write the equation of a line in slope-intercept form that passes through the point \((-4, 5)\) and is perpendicular to the line \(4x + 3y = -24\).

### Step 1: Find the slope of the given line
First, convert the equation \(4x + 3y = -24\) to slope-intercept form (\(y = mx + b\)), where \(m\) is the slope.

Starting with:
\[
4x + 3y = -24
\]
Solve for \(y\):
\[
3y = -4x - 24
\]
\[
y = -\frac{4}{3}x - 8
\]
So, the slope \(m\) of the given line is \(-\frac{4}{3}\).

### Step 2: Find the slope of the perpendicular line
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is:
\[
m_{\text{perpendicular}} = \frac{3}{4}
\]

### Step 3: Write the equation of the line
Now, use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point \((-4, 5)\) and \(m = \frac{3}{4}\).

Substituting the values:
\[
y - 5 = \frac{3}{4}(x + 4)
\]
Distribute the slope:
\[
y - 5 = \frac{3}{4}x + 3
\]
Solve for \(y\):
\[
y = \frac{3}{4}x + 8
\]

### Step 4: Check the answer choices
The correct equation of the line is \(y = \frac{3}{4}x + 8\). This corresponds to **Option A**.

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you find the negative reciprocal of a slope?
2. What is the general form of a line, and how do you convert it to slope-intercept form?
3. Can you find the equation of a line parallel to \(4x + 3y = -24\) passing through a different point?
4. How does the slope-intercept form differ from the point-slope form of a line?
5. What would the equation be if the line was perpendicular to a vertical or horizontal line?

**Tip:** Always double-check the slope when dealing with perpendicular lines to avoid sign errors.

Write the equation of the line in slope-intercept form that passes through (-4, 5) and is perpendicular to 4x + 3y = -24.

Learn how to find the equation of a line in slope-intercept form that passes through the point (-4, 5) and is perpendicular to the line 4x + 3y = -24. This problem involves key algebraic concepts like slope, perpendicular lines, and the point-slope formula. Suitable for students in Grades 9-11.

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