The family of curves given by the equation y = kx + b is characterized by:

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Question: The family of curves given by the equation y = kx + b is characterized by:

Options:

Correct Answer: Both a and b

Solution:

The equation y = kx + b represents a family of straight lines with different slopes (k) and intercepts (b).

The family of curves given by the equation y = kx + b is characterized by:

The family of curves given by the equation y = kx + b is characterized by:

Step 1: Understand that the equation y = kx + b is in the slope-intercept form of a line.
Step 2: Identify that 'k' represents the slope of the line, which determines how steep the line is.
Step 3: Recognize that 'b' represents the y-intercept, which is where the line crosses the y-axis.
Step 4: Realize that by changing the values of 'k' and 'b', you can create different straight lines.
Step 5: Conclude that the equation y = kx + b describes a family of straight lines, each with unique slopes and intercepts.

Linear Equations – The equation y = kx + b represents a linear relationship between x and y, where k is the slope and b is the y-intercept.
Family of Curves – The term 'family of curves' refers to a set of lines that can vary based on the parameters k and b.