Final answer:
The blue graph has the same shape as the red graph, which is a straight line with a slope of 3 and a y-intercept of 9. Therefore, the equation of the blue graph is also y = 3x + 9.
Step-by-step explanation:
To determine the equation of the blue graph, which has the same shape as the red graph depicted in Figure A1, we use the given properties of the red graph. The red graph is a straight line, which suggests that it represents a linear relationship between the variables x and y. The equation of a straight line is typically expressed in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
According to Figure A1, the y-intercept (the point where the line intersects the y-axis) of the red graph is 9, and its slope (the rise over the run) is 3. This means for every unit increase in x, y increases by 3 units. Applying these numbers, the equation for the red graph is y = 3x + 9. Since the blue graph has the same shape as the red graph, its equation will have the same slope and y-intercept, hence, the equation of the blue graph is also y = 3x + 9.
This example clarifies how the slope and the y-intercept are crucial for determining the Algebra of Straight Lines, as they define the line's characteristics on the graph.