To find the slope of the equation, we first need to rearrange it into the standard form of a linear equation, which is generally expressed as:
y = mx + b
In this equation, m represents the slope, and b is the y-intercept. Let’s start with the given equation:
y = 3 + 4x + 5
First, simplify the equation:
y = 4x + (3 + 5)
This simplifies to:
y = 4x + 8
Now that we have the equation in the standard form:
Here, you can see that the coefficient of x is 4. Thus, the slope (m) of the equation is:
m = 4
In conclusion, the slope of the equation y = 4x + 8 is 4. This indicates that for every unit increase in x, y increases by 4 units. Understanding the slope is essential for analyzing the behavior of the linear equation in various contexts, such as graphs, trends, and rates of change.