Find the equation of the family of curves represented by y = mx + c, where m and
Practice Questions
Q1
Find the equation of the family of curves represented by y = mx + c, where m and c are constants.
y = mx + c
y = mx^2 + c
y = c/x + m
y = m^2x + c
Questions & Step-by-Step Solutions
Find the equation of the family of curves represented by y = mx + c, where m and c are constants.
Correct Answer: y = mx + c
Step 1: Understand that 'y = mx + c' is the equation of a straight line.
Step 2: Identify that 'm' represents the slope of the line, which shows how steep the line is.
Step 3: Recognize that 'c' is the y-intercept, which is the point where the line crosses the y-axis.
Step 4: Realize that by changing the values of 'm' and 'c', you can create different lines, which is why it's called a family of curves (or lines in this case).
Step 5: Conclude that the equation 'y = mx + c' describes all possible straight lines that can be formed by varying 'm' and 'c'.
Linear Equations – The equation y = mx + c represents a family of straight lines, where m is the slope and c is the y-intercept.
Parameters of a Line – Understanding how varying m and c affects the position and orientation of the line.
