Linear Functions (\( y = mx + c \))

A linear function is a function that forms a straight line when graphed. It can be written in the form:

\( y = mx + c \)

Where:

• \( m \) = slope (or gradient) of the line
• \( c \) = y-intercept (the point where the line crosses the y-axis)

Features of Linear Functions:

Slope (m): Determines how steep the line is and its direction:

• • If \( m > 0 \), the line slopes upward (increasing function).
  • If \( m < 0 \), the line slopes downward (decreasing function).
  • If \( m = 0 \), the line is horizontal (constant function).

Y-intercept (c): The point where the line meets the y-axis (x = 0).

X-intercept: The point where y = 0, calculated as \( x = -\dfrac{c}{m} \).

• Domain: All real numbers \( (-\infty, \infty) \).
• Range: All real numbers \( (-\infty, \infty) \).
• Graph: Always a straight line.