Final answer:
The question involves mathematics, specifically the relationship between a linear function and its graph. We verify the points given in the table by plugging x-values into the given function to see if the y-values match. The function y=9+3x is another example of how to establish a linear relationship's table and graph.
Step-by-step explanation:
The question is asking to match a given function, y=(2/3)x+4, with a table of values to determine the dependence of y on x. To verify if the values in the table (1,5), (2,10), (3,7), and (4,14) belong to the function, we need to plug each x value into the equation and see if the resulting y values match the ones given.
For instance, if we substitute x=1 into the equation, the calculated y should be 6 2/3, which does not match the given value of 5. Hence, the point (1,5) does not lie on the line represented by the equation y=(2/3)x+4. Similarly, we would calculate the y values for the rest of the provided x values and compare them with the table.
Additionally, the given function y=9+3x represents a line with a slope, or m term, of 3 and a y-intercept, or b term, of 9. By creating a table of values (Table A1) from this function and plotting them on a graph (Figure A1), we can visualize the function as a straight line where each point satisfies the equation.