Final answer:
The slope of a line according to Figure A1 is 3, with a y-intercept of 9, resulting in the equation y = 3x + 9. The slope represents the steepness and direction of the line. The law of reflection states that the angle of incidence equals the angle of reflection, and the slope of the line of reflection would be specific to the given scenario.
Step-by-step explanation:
Understanding the slope of a line and how it is represented in an equation is a fundamental concept in algebra, specifically when dealing with the algebra of straight lines. According to the scenario provided, Figure A1 illustrates a line graph that plots x on the horizontal axis and y on the vertical axis. The y-intercept of the line is 9, indicating that the line crosses the y-axis at the point (0, 9). The slope of this line is given as 3, which means for every one unit increase in x, there is a three-unit increase in y.
The equation of such a straight line is typically expressed in the y = mx + b form, where 'm' represents the slope, and 'b' represents the y-intercept. In this particular example, the slope 'm' is 3, and the y-intercept 'b' is 9, thus the equation of the line would be y = 3x + 9. This form allows for easy comparison and construction of the line on a graph.
In addition to straight lines, reflection is a concept in geometry involving mirror-like reproduction of an object across a line, which is known as the line of reflection. The law of reflection states that the angle of incidence is equal to the angle of reflection, commonly written as θi = θr. However, the slope of the line of reflection itself, when defined, would depend on the context and the specifics of the geometric figure and the angle of incidence.
Considering the algebraic approach to slope and the principles of reflection together, if you were to write an equation like y = mx + b for the line of reflection, the slope would have to be defined by the particular geometric conditions of your reflection scenario.