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Let's solve the equation \( 4x - y = 6 \) to find the slope and the y-intercept of the line.

To find the slope and the y-intercept, we need to rewrite the equation in the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Rearrange the equation into slope-intercept form
Starting with the given equation:
\[
4x - y = 6
\]

Isolate \( y \) by subtracting \( 4x \) from both sides:
\[
-y = -4x + 6
\]

Now, multiply the entire equation by \( -1 \) to make \( y \) positive:
\[
y = 4x - 6
\]

### Step 2: Identify the slope and y-intercept
From the equation \( y = 4x - 6 \), we can directly see:
- The slope (\( m \)) is \( 4 \).
- The y-intercept (\( b \)) is \( -6 \).

### Final Answers:
- Slope: \( 4 \)
- Y-intercept: \( -6 \)

Let me know if you want further details or if you have any questions!

Here are five related questions to explore further:
1. How do you find the slope if the equation is in standard form \( Ax + By = C \)?
2. What is the slope of a horizontal line?
3. How do you find the equation of a line given a point and the slope?
4. What does a slope of zero represent graphically?
5. How does changing the slope affect the steepness of the line?

**Tip:** Always try to express the equation in slope-intercept form to quickly identify both the slope and the y-intercept.

Find the slope and the y-intercept of the line 4x - y = 6. Write your answers in simplest form.

Solve for the slope and y-intercept of the linear equation 4x - y = 6. This step-by-step solution explains how to convert the equation into slope-intercept form, making it ideal for students in Grades 7-9.

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