Final answer:
A linear graph refers to a straight line represented by the equation y = mx + b or y = a + bx, with a constant slope and y-intercept. If there is a tiny curve in the graph, the relationship may be almost linear but not perfectly so.
Step-by-step explanation:
The term linear in mathematics refers to the nature of a graph as it relates to an equation. When the equation of a line is in the form y = mx + b or y = a + bx, where m and b (or a and b in the context of statistics) are constants, the graph is expected to be a straight line. This linear graph shows a direct relationship where the slope (m or b) is consistent across the entire line.
In a linear relationship, for every unit increase in the independent variable x, the dependent variable y increases by the slope amount. The y-intercept is where the graph intersects the y-axis, which is the point on the graph where x equals zero. If you notice a curve, even a slight one, in the graph of a data set that was expected to be linear, it means that the relationship may not be perfectly linear but could be almost linear depending on the context of the data and the scale of the curve.
In the given example with a y-intercept of 9 and a slope of 3, indicating a rise of 3 units on the y-axis for every 1 unit increase on the x-axis, this describes a perfect straight line where these values are constant. A perfectly straight line doesn't feature any curve. If there's a tiny curve, this indicates the possibility of a slight nonlinear relationship.