The gradient shows the rate at which y changes as x changes. A positive gradient means y increases when x increases, while a negative gradient indicates a decrease. Its numerical value allows comparisons between relationships and supports predictions of how one quantity responds to another.
The y-intercept identifies the value of y when x equals zero. It provides a starting point for interpreting the relationship and helps distinguish graphs that have the same gradient but different initial values. Together, the gradient and intercept specify the linear equation represented by the graph.
Equal changes in x should produce equal changes in y when the rate is constant. On the graph, this pattern appears as points that follow one straight path rather than a curve. A straight-line pattern therefore helps users recognize consistent change and separate linear relationships from patterns whose rates vary.
First identify the horizontal x-coordinate and then the vertical y-coordinate for each ordered pair. Mark every pair at the position where those coordinate values meet, then connect points that satisfy the same linear equation. Checking several points helps reveal plotting errors and confirms whether they follow a straight-line pattern.
The gradient can be determined from how much y changes compared with x, while the y-intercept is read where the graph crosses the vertical axis. These two features provide the values of m and b in y = mx + b. Substituting plotted points into the equation then checks whether the graph and equation agree.
They are useful when two quantities have a linear relationship and a constant rate of change. A graph can help compare data sets, display patterns, calculate rates, and estimate values not directly shown. In scientific and mathematical contexts, this visual representation makes relationships easier to interpret and supports prediction from existing data.