Question
find if each equation is proportional, if so what is their constant of proportionality
1: y=6x+7
2. y=-2/5x
1: y=6x+7
2. y=-2/5x
Answers
GPT-4o mini
To determine if each equation is proportional, we need to check whether the equation can be expressed in the form \(y = kx\), where \(k\) is a constant. Proportional relationships pass through the origin (0, 0).
1. **Equation:** \(y = 6x + 7\)
This equation is not in the form \(y = kx\) because of the +7. It represents a linear equation that intercepts the y-axis at 7. Thus, it does not pass through the origin (0, 0), and is therefore **not proportional**.
2. **Equation:** \(y = -\frac{2}{5}x\)
This equation is in the form \(y = kx\) where \(k = -\frac{2}{5}\). Since it passes through the origin, it is **proportional**. The constant of proportionality is \(-\frac{2}{5}\).
### Summary:
1. Not proportional
2. Proportional with a constant of proportionality of \(-\frac{2}{5}\)
1. **Equation:** \(y = 6x + 7\)
This equation is not in the form \(y = kx\) because of the +7. It represents a linear equation that intercepts the y-axis at 7. Thus, it does not pass through the origin (0, 0), and is therefore **not proportional**.
2. **Equation:** \(y = -\frac{2}{5}x\)
This equation is in the form \(y = kx\) where \(k = -\frac{2}{5}\). Since it passes through the origin, it is **proportional**. The constant of proportionality is \(-\frac{2}{5}\).
### Summary:
1. Not proportional
2. Proportional with a constant of proportionality of \(-\frac{2}{5}\)