y=
− 
2
3
​
 x+8
y, equals, x, plus, 8
y=
x+8

It seems like you've written two different linear equations:

1. \( y = -\frac{2}{3}x + 8 \)
2. \( y = x + 8 \)

Each of these is the equation of a line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### 1. For the equation \( y = -\frac{2}{3}x + 8 \):
- **Slope**: \( -\frac{2}{3} \)
- **Y-intercept**: \( 8 \)

### 2. For the equation \( y = x + 8 \):
- **Slope**: \( 1 \) (since \( y = 1x + 8 \))
- **Y-intercept**: \( 8 \)

These two lines have the same y-intercept but different slopes, meaning they intersect at \( (0, 8) \), but have different inclinations.

Would you like to explore how to graph these, or solve for where they intersect?

---

Here are some related questions to explore:

1. What is the point of intersection between these two lines?
2. How can we graph both lines on the same coordinate plane?
3. What happens when the slopes of two lines are equal or different?
4. Can we solve for \(x\) when both equations are equal?
5. How does the slope affect the steepness of a line?

**Tip**: The slope determines the direction and steepness of the line—negative slopes go downward, and positive slopes go upward!

The query submitted by the user: y = -2/3x + 8; y = x + 8

Explore the slope and y-intercept of two linear equations: y = -2/3x + 8 and y = x + 8. Learn how to find their slopes, y-intercepts, and the point of intersection. This lesson is suitable for students in Grades 8-10, covering core algebraic concepts and equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation