Find an equation of the line that satisfies the given conditions. Through \( (3,9) \); parallel to the x-axis Need Help? Read it Whtch It

To find the equation of a line that **passes through the point \((3, 9)\)** and is **parallel to the x-axis**, follow these steps: ### Understanding the Properties 1. **Parallel to the x-axis:** - A line parallel to the x-axis has the same y-coordinate for all points on the line. - This means the y-value remains constant, regardless of the x-value. 2. **Passing through \((3, 9)\):** - Since the line must pass through the point \((3, 9)\), the y-coordinate for the entire line will be **9**. ### Formulating the Equation Given the above properties, the equation of the line is: \[ y = 9 \] ### Explanation - **y = 9** means that for any value of \(x\), the value of \(y\) will always be 9. - This fits the condition of being parallel to the x-axis (since y is constant) and passing through the point \((3, 9)\). ### Graphical Representation Here's a simple graph to illustrate the line: ``` y | | |------------------------- y = 9 | | |__________________________ x ``` All points on the line \(y = 9\) will have \(y\)-coordinate equal to 9, no matter what the \(x\)-coordinate is. ### Final Answer The equation of the desired line is: \[ \boxed{y = 9} \]