Jordan has the linear equation y – 9 = 3(x + 12) on her math homework. Determine whether each statement is a true or false statement about the equation. Select the correct answer in each row.
 
 	True	False
The line passes through the point (‒9, 12).	□
□
The slope of the line is 3.	□
□
The line passes through the point (‒12, 9).	□
□


Let's break down the given linear equation and analyze each statement.

### Step 1: Simplify the equation
The given equation is:
\[
y - 9 = 3(x + 12)
\]
Distribute the \(3\) on the right-hand side:
\[
y - 9 = 3x + 36
\]
Now, add 9 to both sides to solve for \(y\):
\[
y = 3x + 45
\]
This is the equation of a line in slope-intercept form \(y = mx + b\), where:
- \(m\) is the slope, and
- \(b\) is the y-intercept.

In this case, the slope \(m = 3\) and the y-intercept \(b = 45\).

### Step 2: Evaluate each statement

1. **The line passes through the point (‒9, 12).**

   To check this, substitute \(x = -9\) and \(y = 12\) into the equation \(y = 3x + 45\):
   \[
   12 = 3(-9) + 45
   \]
   \[
   12 = -27 + 45
   \]
   \[
   12 = 18
   \]
   This is **false**, so the line **does not** pass through the point (‒9, 12).

2. **The slope of the line is 3.**

   The equation \(y = 3x + 45\) has a slope of 3. This is **true**.

3. **The line passes through the point (‒12, 9).**

   Substitute \(x = -12\) and \(y = 9\) into the equation \(y = 3x + 45\):
   \[
   9 = 3(-12) + 45
   \]
   \[
   9 = -36 + 45
   \]
   \[
   9 = 9
   \]
   This is **true**, so the line **does** pass through the point (‒12, 9).

### Final Answers:
- The line passes through the point (‒9, 12): **False**
- The slope of the line is 3: **True**
- The line passes through the point (‒12, 9): **True**

---

Do you want further details on how I derived these conclusions? Here are some related questions to explore further:

1. How do you find the y-intercept from a linear equation?
2. What is the point-slope form of a linear equation, and how is it useful?
3. How can you verify if a point lies on a given line algebraically?
4. What is the geometric interpretation of the slope of a line?
5. Can the equation of a line have a different slope while still passing through the same points?

**Tip:** Always substitute the coordinates of a point into the equation to check if it lies on the line.

Jordan has the linear equation y – 9 = 3(x + 12) on her math homework. Determine whether each statement is a true or false statement about the equation.

True	False
The line passes through the point (‒9, 12). 
The slope of the line is 3.
The line passes through the point (‒12, 9).

Explore how to solve the linear equation y – 9 = 3(x + 12) and determine the truth of various statements regarding slope and points on the line. This detailed explanation includes checking if the line passes through points like (‒9, 12) and understanding the slope of the line. Suitable for students in Grades 8-10.

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