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

Practice Questions

Q1
The family of curves given by the equation y = kx + b is characterized by:
  1. Different slopes
  2. Different intercepts
  3. Both a and b
  4. None of the above

Questions & Step-by-Step Solutions

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.
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