Pregunta
What is the \( y \)-intercept in the equation? \[ y=(-2 / 3) x+8 \]
Ask by Mccoy Chang. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The \( y \)-intercept is 8.
Solución
The given equation is in the slope-intercept form:
\[
y = mx + b
\]
where:
- \( m \) is the slope,
- \( b \) is the \( y \)-intercept.
For the equation:
\[
y = \left( -\frac{2}{3} \right) x + 8
\]
- The slope \( m \) is \( -\frac{2}{3} \).
- The \( y \)-intercept \( b \) is **8**.
**Therefore, the \( y \)-intercept is \( 8 \).**
This means that the graph of the equation crosses the \( y \)-axis at the point \( (0, 8) \).
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Simplifique esta solución Extra Insights
The \( y \)-intercept of a linear equation is the point where the graph intersects the \( y \)-axis. In the case of the equation \( y = \left(-\frac{2}{3}\right)x + 8 \), when \( x = 0 \), the equation simplifies to \( y = 8 \). Therefore, the \( y \)-intercept is \( 8 \), which means the graph crosses the \( y \)-axis at the point \( (0, 8) \). To visualize this, imagine a straight line that slopes downward as it moves from left to right, starting from \( 8 \) on the \( y \)-axis. If you were to plot it, you'd see that at the point \( (0, 8) \), the line crosses the \( y \)-axis. It's like the line says, "Hey, I’m here at this height when there's no horizontal movement!"
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