Final answer:
The equation y = kx represents a linear relationship with k being the slope of the line. In y = 9 + 3x, 3 is the slope, and 9 is the y-intercept where the line crosses the y-axis. Exponential growth increases at a rate that becomes faster with each increment of the dependent variable.
Step-by-step explanation:
The equation y = kx is a linear relationship where k represents the slope of the line and x represents the independent variable. When k is a constant number like 3, the equation becomes y = 3x. Here, for every unit increase in x, y increases by 3, indicating a consistent rise over run that characterizes a straight line. In contrast to linear growth, exponential growth indicates that as the value of the dependent variable increases, the rate at which it grows also increases, exemplified by bacteria reproducing at an increasing rate generation after generation.
The equation y = 9 + 3x includes both a slope and a y-intercept. The y-intercept is where the line crosses the y-axis, which is 9 in this case. The slope of the line, represented by the coefficient of x, is 3. This means for every one unit increase in x, y will increase by 3 units. To visualize this, one would plot a series of (x, y) points on a graph based on this equation and draw a line through these points.