Function B has a steeper slope of -4.5 than Function A, which has a rate of change of 2. Therefore, Function B has a greater rate of change.
To determine which function has a greater rate of change, we compare the slopes of Function A and Function B. Function A has a rate of change of 2, which means for every unit increase in x, the value of y increases by 2. On the other hand, Function B is defined by the equation y = −4.5x + 15, and here the coefficient of x, which is −4.5, represents its slope or rate of change. Since slope describes the steepness of the line, and the slope of Function B has a greater absolute value than the slope of Function A, we can conclude that Function B has a steeper and therefore a greater rate of change.
Using the information provided in the examples regarding the algebra of straight lines, we can infer that the slope or 'm' term in the linear equation dictates this rate. Additionally, if we refer to Figure A1, which describes a slope of 3, it provides a visual example of a positive slope where there is a rise of 3 units for every increase of 1 unit along the x-axis. The larger the slope value, the steeper the line. In conclusion, Function B has a more significant rate of change compared to Function A.