Question

10 What is the equation in slope-intercept form of the line that crosses the x-axis at 36 and is perpendicular to the line represented by y = - 4/9 * x + 5
Q
3 y = 9/4 * x - 81
y = 4/9 * x - 16
F y = 4/9 * x + 16
H y = 9/4 * x + 81

Answer 1

To find the equation of the line that crosses the x-axis at 36 and is perpendicular to the given line \( y = -\frac{4}{9}x + 5 \), follow these steps:

1. **Find the slope of the given line \( y = -\frac{4}{9}x + 5 \)**:
- The slope \( m_1 \) of this line is \( -\frac{4}{9} \).

2. **Determine the slope of the line perpendicular to this line**:
- The slope \( m_2 \) of a line perpendicular to another is the negative reciprocal of the slope of the original line.
- Thus, \( m_2 = -\frac{1}{m_1} = -\frac{1}{-\frac{4}{9}} = \frac{9}{4} \).

3. **Use the point where it crosses the x-axis**:
- The line crosses the x-axis at \( x = 36 \), which means at this point \( y = 0 \).
- Thus, the point we can use is \( (36, 0) \).

4. **Use the point-slope form of the equation to find the line's equation**:
- The point-slope form is given by \( y - y_1 = m(x - x_1) \).
- Substituting \( m = \frac{9}{4} \), \( x_1 = 36 \), and \( y_1 = 0 \):
\[
y - 0 = \frac{9}{4}(x - 36)
\]
\[
y = \frac{9}{4}x - \frac{9}{4} \times 36
\]
\[
y = \frac{9}{4}x - 81
\]

Therefore, the equation of the line in slope-intercept form is:
\[
y = \frac{9}{4}x - 81
\]

**The correct answer is:**
\[
\text{H } y = \frac{9}{4}x - 81
\]