Question

write the slope intercept form of the equation of the line described.
through: (0,-5) perp. to y=-1/9x+5

Answer 1

To find the slope-intercept form of the equation of the line that is perpendicular to \( y = -\frac{1}{9}x + 5 \) and goes through the point \( (0, -5) \), we can follow these steps:

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

2. **Find the slope of the perpendicular line**: The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope \( m \) of the line we are looking for is:
\[
m = -\frac{1}{(-\frac{1}{9})} = 9
\]

3. **Use the point-slope form**: We have the slope \( m = 9 \) and the point \( (0, -5) \). We can use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = 9 \), \( x_1 = 0 \), and \( y_1 = -5 \):
\[
y - (-5) = 9(x - 0)
\]
Simplifying this, we get:
\[
y + 5 = 9x
\]
\[
y = 9x - 5
\]

4. **Final result**: The slope-intercept form of the equation of the line is:
\[
y = 9x - 5
\]