Linear Equations 492653

1. **State the problem:** Determine if each given equation is linear. 2. **Recall the definition:** A linear equation in one variable $x$ has the form $y = mx + b$, where $m$ and $b$ are constants, and the variable $x$ is to the first power only. 3. **Analyze each equation:** (a) $y = x^2 + 7$ - The term $x^2$ has $x$ raised to the power 2. - Since the power is not 1, this is **not linear**. (b) $y = x + 9$ - The term $x$ is to the first power. - This matches the form $y = mx + b$ with $m=1$, $b=9$. - This is **linear**. (c) $y = 4^x$ - The variable $x$ is in the exponent. - This is an exponential function, not linear. - So, **not linear**. (d) $y = -2x^3$ - The term $x^3$ has $x$ raised to the power 3. - Since the power is not 1, this is **not linear**. **Final answers:** - (a) No - (b) Yes - (c) No - (d) No