The shape of a graph of a linear relationship is a straight line.
A linear relationship, by definition, exhibits a constant rate of change. This constant rate of change, when plotted on a coordinate plane, results in a straight line. The line can slope upwards (positive relationship), downwards (negative relationship), be horizontal (zero slope), or even vertical (undefined slope), but it will always be a straight line. The x and y coordinates have a direct, unchanging relationship expressed in the form of a linear equation (e.g., y = mx + b).
For example:
- The equation
y = 2x + 1represents a linear relationship. If you were to plot various (x, y) coordinate pairs that satisfy this equation, they would all fall on a single straight line.
Therefore, the defining characteristic of a graph representing a linear relationship is its linearity; it's a straight line, illustrating the direct and constant connection between the two variables.
