Final answer:
The graph of a line described by the equation y = a + bx is a straight line, where the slope 'b' and the y-intercept 'a' determine the line's angle and where it crosses the y-axis. Understanding these variables enables one to predict the graph's appearance without plotting points.
Step-by-step explanation:
Yes, you can predict what the graph of a line will look like without finding points or graphing it if you understand the general equation of a line. The graph of a linear equation in the form y = a + bx is always a straight line, where a is the y-intercept and b is the slope. The slope determines the angle of the line with respect to the x-axis, and the y-intercept determines where the line crosses the y-axis.
For example, if a is positive and b is positive, the line will cross the y-axis above the origin and will rise as it moves from left to right. If a is negative and b is also negative, the line will cross below the origin and will fall as it moves from left to right.
A line graph, which can be used in economic models, shows the relationship between two variables. By understanding the equation's variables, one can determine the behavior of the graph without plotting actual data points. The trend line in a graph represents the overall direction that the data points seem to indicate, and even though real data may have some inaccuracies, it can still tell us a lot about the trend that the data represents.