The function $P(x) = 2x + 5$ is a linear function. Here’s a breakdown of its key components:

1. Slope (m): The coefficient of $x$ is 2, which means the slope of the line is 2. This indicates that for every unit increase in $x$, the value of $P(x)$ increases by 2.

2. Y-intercept (b): The constant term is 5, which is the y-intercept. This means that when $x = 0$, $P(x) = 5$.

3. Graph: The graph of this function would be a straight line with a slope of 2, intersecting the y-axis at the point (0, 5).

4. Domain and Range:

   • The domain (all possible values of $x$) is all real numbers, $\mathbb{R}$.
   • The range (all possible values of $P(x)$) is also all real numbers, $\mathbb{R}$.

5. Rate of Change: The rate of change of $P(x)$ with respect to $x$ is constant and equal to the slope, which is 2.

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the x-intercept of $P(x) = 2x + 5$?
2. What does the slope of 2 represent in real-world applications?
3. How would the graph change if the slope were negative?
4. What would the function look like if the y-intercept were 0 instead of 5?
5. How can we determine if two linear functions are parallel or perpendicular?

Tip: When graphing a linear function, always start by plotting the y-intercept and then use the slope to determine the direction and steepness of the line.