Discover the linear relationship between X and Y in the equation Y = W*X + B. Learn how changes in W and B affect the values of X and Y, and gain a deeper understanding of this fundamental mathematical concept.
Table of Contents
Question
Two values X and Y are related as shown
Y = W*X + B
Identify the correct statement
A. Y is the provided input, and X is the calculated output
B. Y does not change with a change in B
C. X and Y have a linear relationship
Answer
C. X and Y have a linear relationship
Explanation
In the given equation, Y = W*X + B, the variables X and Y are related in a linear fashion. This means that if you plot the values of X and Y on a graph, they will form a straight line.
Here’s a detailed explanation of why the other options are incorrect:
A. Y is the provided input, and X is the calculated output – This statement is false. In the equation, X is the independent variable (input), and Y is the dependent variable (output). The value of Y is calculated based on the values of W, X, and B.
B. Y does not change with a change in B – This is also false. The variable B represents the y-intercept, which is the point where the line crosses the y-axis. Changing the value of B will shift the line up or down on the y-axis, thus changing the value of Y for any given X.
In the linear equation Y = W*X + B:
- W represents the slope or gradient of the line, which determines how steeply the line rises or falls.
- X is the independent variable, meaning its value is not dependent on other variables in the equation.
- B is the y-intercept, which is the value of Y when X equals zero.
By understanding the roles of W, X, and B in this linear equation, you can better grasp the relationship between X and Y and how changes in these variables affect the graph of the line.
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