Question
Find the slope and \( y \)-intercept of the following linear equation. Express the \( y \)-intercept as a coordinate pair. \[ y=-\frac{3}{4} x \]
Ask by Davey Malone. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The slope is \( -\frac{3}{4} \) and the \( y \)-intercept is \( (0, 0) \).
Solution
To analyze the linear equation \( y = -\frac{3}{4}x \), we'll identify its **slope** and **\( y \)-intercept**.
### 1. Slope (\( m \))
The slope-intercept form of a linear equation is:
\[ y = mx + b \]
where:
- \( m \) is the slope
- \( b \) is the \( y \)-intercept
Comparing with the given equation \( y = -\frac{3}{4}x \):
- The coefficient of \( x \) is \( -\frac{3}{4} \), which means:
\[
\text{Slope (} m \text{)} = -\frac{3}{4}
\]
### 2. \( y \)-Intercept (\( b \))
In the absence of a constant term, the equation can be rewritten as:
\[ y = -\frac{3}{4}x + 0 \]
This shows that the \( y \)-intercept (\( b \)) is \( 0 \).
Expressed as a coordinate pair:
\[
\text{\( y \)-intercept} = (0, 0)
\]
### **Summary**
- **Slope:** \( -\frac{3}{4} \)
- **\( y \)-intercept:** \( (0, 0) \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
The slope of the given linear equation \( y = -\frac{3}{4} x \) is \(-\frac{3}{4}\). This means that for every 4 units you move to the right on the \( x \)-axis, the line moves down 3 units on the \( y \)-axis. To find the \( y \)-intercept, set \( x = 0 \). Plugging this into the equation gives \( y = -\frac{3}{4}(0) = 0 \). Therefore, the \( y \)-intercept as a coordinate pair is \( (0, 0) \).
