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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:
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Practice Questions
1 question
Q1
The family of curves given by the equation y = kx + b is characterized by:
Different slopes
Different intercepts
Both a and b
None of the above
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The equation y = kx + b represents a family of straight lines with different slopes (k) and intercepts (b).
Questions & Step-by-step Solutions
1 item
Q
Q: The family of curves given by the equation y = kx + b is characterized by:
Solution:
The equation y = kx + b represents a family of straight lines with different slopes (k) and intercepts (b).
Steps: 5
Show Steps
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.
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