Linear equation

Property A linear equation is an equation whose graph is a line. A linear function is a function whose graph is a line and can be written in the form $f(x) = mx + b$, where $m$ and $b$ are real numbers.

Examples The equation $y = x + 3$ is linear. Plotting points like $(0, 3)$ and $(1, 4)$ will form a straight line on a graph. The car wash fundraiser follows the rule $f(x) = 5x 4$. Since the graph is a straight line, it represents a linear function. An equation like $y = x + 10$ is linear because for every one unit you move right, you move one unit down, creating a straight line.

Explanation Think of a linear function as a perfectly straight path! For every step you take sideways (the x value), you go up or down by the exact same amount (the slope). This consistency creates a straight line, not a wild curve. We can map out this predictable journey by plotting a few points from a table and connecting them.