Find the family of curves represented by the equation y = mx + c, where m and c

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Question: Find the family of curves represented by the equation y = mx + c, where m and c are constants.

Options:

Correct Answer: Straight lines with varying slopes and intercepts

Solution:

The equation y = mx + c represents straight lines where m is the slope and c is the y-intercept.

Find the family of curves represented by the equation y = mx + c, where m and c are constants.

Find the family of curves represented by the equation y = mx + c, where m and c are constants.

Correct Answer: y = mx + c represents a family of straight lines.

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'.

Linear Equations – The equation y = mx + c represents a family of straight lines characterized by varying slopes (m) and y-intercepts (c).
Slope-Intercept Form – The equation is in slope-intercept form, which is a common way to express linear equations.