https://file.aiquickdraw.com/mathbot/file/1726148621620lz7uec4r.jpg

To solve this problem, we need to identify the equation that represents a line parallel to \( y = 8x - 4 \).

### Step 1: Understand the properties of parallel lines
Parallel lines have the same slope. The equation \( y = 8x - 4 \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m = 8 \).

### Step 2: Check the slopes of the given equations
We will rewrite each of the provided equations to slope-intercept form, \( y = mx + b \), and identify their slopes.

1. **Option 1: \( x + 8y = -16 \)**
   \[
   8y = -x - 16 \quad \Rightarrow \quad y = -\frac{1}{8}x - 2
   \]
   Slope: \( m = -\frac{1}{8} \) (Not parallel).

2. **Option 2: \( x - 8y = -40 \)**
   \[
   -8y = -x - 40 \quad \Rightarrow \quad y = \frac{1}{8}x + 5
   \]
   Slope: \( m = \frac{1}{8} \) (Not parallel).

3. **Option 3: \( y - 8x = -1 \)**
   \[
   y = 8x - 1
   \]
   Slope: \( m = 8 \) (Parallel).

4. **Option 4: \( 8x + y = 3 \)**
   \[
   y = -8x + 3
   \]
   Slope: \( m = -8 \) (Not parallel).

### Conclusion:
The equation that represents a line parallel to \( y = 8x - 4 \) is **\( y - 8x = -1 \)** (Option 3).

Would you like more details, or do you have any questions?

Here are 5 related questions you might want to explore:
1. How do we determine if two lines are perpendicular instead of parallel?
2. What is the significance of the y-intercept in the equation of a line?
3. How can we convert any general linear equation into slope-intercept form?
4. What happens to the slope when we reflect a line over the x-axis?
5. Can two lines with different y-intercepts ever intersect if they are parallel?

**Tip:** Remember, two lines are parallel if and only if they have the same slope.

Which equation represents a line which is parallel to the line y = 8x - 4?

Find out how to identify the equation of a line parallel to y = 8x - 4. This problem focuses on the properties of parallel lines, slope-intercept form, and finding slopes. Perfect for high school students studying algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation