Find the family of curves represented by the equation y = mx + c, where m and c are constants.
Practice Questions
1 question
Q1
Find the family of curves represented by the equation y = mx + c, where m and c are constants.
Straight lines with varying slopes and intercepts
Parabolas with varying vertices
Circles with varying radii
Ellipses with varying axes
The equation y = mx + c represents straight lines where m is the slope and c is the y-intercept.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the family of curves represented by the equation y = mx + c, where m and c are constants.
Solution: The equation y = mx + c represents straight lines where m is the slope and c is the y-intercept.
Steps: 5
Step 1: Understand the equation y = mx + c. Here, 'y' is the output value, 'x' is the input value, 'm' is the slope of the line, and 'c' is the y-intercept.
Step 2: Recognize that 'm' (slope) determines how steep the line is. A larger 'm' means a steeper line.
Step 3: Understand that 'c' (y-intercept) is where the line crosses the y-axis. If 'c' is 0, the line goes through the origin (0,0).
Step 4: Realize that by changing the values of 'm' and 'c', you can create different straight lines. This means there are many possible lines (a family of curves) represented by this equation.
Step 5: Conclude that the equation y = mx + c describes all straight lines in a 2D plane, where each line is defined by specific values of 'm' and 'c'.
