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Persamaan garis yang melalui titik (8,-2) dan tegak lurus garisgradien ¾ adalah

To solve this problem, we need to determine the equation of a line passing through the point \((8, -2)\) and perpendicular to a line with a gradient of \( \frac{3}{4} \).

### Step-by-step process:

1. **Perpendicular Gradient:**
   - If two lines are perpendicular, their gradients are negative reciprocals. Given the gradient \( m_1 = \frac{3}{4} \), the gradient of the perpendicular line, \( m_2 \), would be:
   \[
   m_2 = -\frac{4}{3}
   \]

2. **Equation of the Line:**
   The general form of the equation of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Where \(m\) is the gradient and \((x_1, y_1)\) is the point the line passes through. Substituting \( m = -\frac{4}{3} \) and \((x_1, y_1) = (8, -2)\):
   \[
   y - (-2) = -\frac{4}{3}(x - 8)
   \]
   Simplifying:
   \[
   y + 2 = -\frac{4}{3}(x - 8)
   \]
   Multiply both sides by 3 to eliminate the fraction:
   \[
   3(y + 2) = -4(x - 8)
   \]
   Distribute:
   \[
   3y + 6 = -4x + 32
   \]
   Rearrange into the standard form \(Ax + By + C = 0\):
   \[
   4x + 3y - 26 = 0
   \]

This is the equation of the line. Comparing with the options provided, the correct answer is **C: \( 4x + 3y - 26 = 0 \)**.

### Do you want further details or have any questions?

### Related questions:
1. How do you find the slope of a line from two points?
2. What is the significance of negative reciprocals in perpendicular lines?
3. Can you derive the equation of a line parallel to another line?
4. How do you convert a line equation from point-slope form to standard form?
5. What does the gradient of a line represent in real-life problems?

#### Tip: Always check if the equation is in its simplest form and aligns with the provided options.

Persamaan garis yang melalui titik (8, -2) dan tegak lurus garis dengan gradien 3/4 adalah

Learn how to determine the equation of a line passing through point (8, -2) and perpendicular to a line with gradient 3/4. This solution uses core geometry concepts such as negative reciprocal slopes and linear equations, making it ideal for students in Grades 9-11.

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