Write the equation of a line that passes through the point
(
−
18
,
−
7
)
 and is perpendicular to the line 
9
x
−
7
y
=
−
14
. Write your answer in slope-intercept form
  

To find the equation of the line that passes through the point \((-18, -7)\) and is perpendicular to the line \(9x - 7y = -14\), we need to follow these steps:

### Step 1: Find the slope of the given line
First, let's write the equation \(9x - 7y = -14\) in slope-intercept form \(y = mx + b\).

Start by isolating \(y\):
\[
9x - 7y = -14
\]
\[
-7y = -9x - 14
\]
\[
y = \frac{9}{7}x + 2
\]
So, the slope (\(m\)) of the given line is \(\frac{9}{7}\).

### Step 2: Determine the slope of the perpendicular line
The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. 

The slope of the perpendicular line will be:
\[
m_{\text{perpendicular}} = -\frac{7}{9}
\]

### Step 3: Use the point-slope form to write the equation
We 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 \((-18, -7)\) and \(m\) is \(-\frac{7}{9}\).

Substituting the values:
\[
y - (-7) = -\frac{7}{9}(x - (-18))
\]
\[
y + 7 = -\frac{7}{9}(x + 18)
\]

### Step 4: Simplify to slope-intercept form
Distribute and simplify the equation to put it in slope-intercept form \(y = mx + b\):
\[
y + 7 = -\frac{7}{9}x - \frac{7}{9} \times 18
\]
\[
y + 7 = -\frac{7}{9}x - 14
\]
\[
y = -\frac{7}{9}x - 14 - 7
\]
\[
y = -\frac{7}{9}x - 21
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
y = -\frac{7}{9}x - 21
\]

Would you like further details or have any questions?

---

Here are some related questions to explore:

1. How do you find the slope of a line given two points?
2. What is the relationship between the slopes of parallel lines?
3. How do you find the point of intersection between two lines?
4. What is the general form of a linear equation, and how can you convert it to slope-intercept form?
5. How does the slope-intercept form of an equation help in graphing a line?

**Tip:** When working with perpendicular lines, remember that their slopes are negative reciprocals of each other.

Write the equation of a line that passes through the point (-18, -7) and is perpendicular to the line 9x - 7y = -14. Write your answer in slope-intercept form.

Learn how to find the equation of a line passing through the point (-18, -7) and perpendicular to 9x - 7y = -14. This problem demonstrates key concepts like slope-intercept form, perpendicular lines, and the point-slope formula. Ideal for students in Grades 9-11.

Math Problem Statement

Write the equation of a line that passes through the point ( − 18 , − 7 ) and is perpendicular to the line 9 x − 7 y

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