Question
\( y=\frac{2}{3} x+3 \) Slope \( (m): \square \) \( y \)-intercept \( (b): \square \)
Ask by Gordon Wade. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Slope (\( m \)): \( \frac{2}{3} \)
\( y \)-intercept (\( b \)): \( 3 \)
Solution
Sure! Let's identify the slope and the \( y \)-intercept from the given linear equation.
**Given Equation:**
\[ y = \frac{2}{3}x + 3 \]
This equation is in the **slope-intercept form**, which is:
\[ y = mx + b \]
where:
- \( m \) is the **slope** of the line.
- \( b \) is the **\( y \)-intercept**, the point where the line crosses the \( y \)-axis.
**Identifying the Components:**
- **Slope (\( m \)):** This is the coefficient of \( x \).
\[ m = \frac{2}{3} \]
- **\( y \)-intercept (\( b \)):** This is the constant term.
\[ b = 3 \]
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**Filled In:**
\[ y = \frac{2}{3}x + 3 \]
- **Slope (\( m \)):** \( \frac{2}{3} \)
- **\( y \)-intercept (\( b \)):** \( 3 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
The slope \( (m) \) of the given linear equation, \( y = \frac{2}{3} x + 3 \), is \( \frac{2}{3} \). This means for every increase of 3 units in \( x \), \( y \) goes up by 2 units. It's like climbing a hill that rises gently but steadily—perfect for those scenic walks! The \( y \)-intercept \( (b) \) of the equation is \( 3 \). This is where the line crosses the \( y \)-axis, meaning if you were to plot this line, it would hit the \( y \)-axis at the point \( (0, 3) \). Imagine marking that spot on a map—it's your starting point on this slopey adventure!
