Y = 2x – 4
What’s the initial value
The Correct Answer and Explanation is:
To identify the initial value in the equation ( Y = 2x – 4 ), let’s first understand the components of the equation. This equation is written in the form of a linear equation, which generally follows the format:
[
Y = mx + b
]
where:
- ( m ) is the slope of the line, representing the rate of change of ( Y ) with respect to ( x ),
- ( b ) is the initial value (or the y-intercept) of the line.
The initial value, or y-intercept, is the point where the line crosses the y-axis, which occurs when ( x = 0 ). In this case, the equation ( Y = 2x – 4 ) has a slope ( m = 2 ) and a y-intercept ( b = -4 ).
Finding the Initial Value
To confirm the initial value, we can substitute ( x = 0 ) into the equation:
[
Y = 2(0) – 4
]
[
Y = 0 – 4
]
[
Y = -4
]
Thus, the initial value is ( -4 ).
Explanation of the Initial Value
In a linear equation like ( Y = 2x – 4 ), the initial value represents the starting point or baseline value of ( Y ) when ( x ) is zero. This value is significant because it provides a reference point for the entire line. In a graph, the point ( (0, -4) ) indicates where the line crosses the y-axis.
The initial value tells us that, without any increase in ( x ) (when ( x ) is zero), the value of ( Y ) begins at ( -4 ). This starting point is useful in real-world contexts because it often represents the base amount or initial condition before any changes due to the slope (rate of change) come into effect.
Understanding the initial value and the slope together allows us to predict and interpret how ( Y ) changes as ( x ) increases or decreases. Here, for each increase of 1 in ( x ), ( Y ) increases by 2, and the starting position for this increase is ( Y = -4 ).