Choices 2 and 3 (READ ALL EXPLANATIONS)
Step-by-step explanation:
To find out the rate of changes for Bush A, you have to choose coordinate points from the graph that hit the line. Then after doing so, you have (1,12) (3,16) and (5,20). You then have to subtract both the x and y values from each other to get your rate of change. Resulting in 4/2, which when simplified is 2. From there you can start building your slope-intercept form equation. Now that you have your rate of change, you then have to find out the initial height of the bush before it started growing. Mathematically worded as the y-intercept. To find the y-intercept from a graph you look at the y axis and see which number hit the line from there. An approximate estimate would be 10. Your finished equation for Bush A should look like y=2x+10. The next equation you want to form is your Bush B one. However, the information you need is already provided to create your equation, y=2.5x+7.5. Now that you have both your equations for both bushes you can look at the statements below to see which answers are corrects based on your data. The first statement is incorrect because Bush A's rate of change is 2 and Bush B's is 2.5. Therefore Bush B's rate of change is bigger not vise versa. The second statement is correct because Bush B's initial value or y-intercept is 7.5 and Bush A's is 10. Therefore, Bush B's initial value is less than that of Bush A's. The third statement is also correct because after substituting the 7 from the 7 years into both equations because the x is the number of years the plant has grown from the original height, Bush A's result was 24 and Bush B's result was 25. Therefore Bush B would be 1 inch taller in that time frame.
