Question

Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer.

Answer 1

A table of data for two different linear functions using the same values of x for both functions is shown below:

$\begin{tabular} {|c|c|c|} x&y=2x+7&y=-x+4\\[1ex] -3&2(-3)+7=-6+7=1&-(-3)+4=3+4=7\\ -2&2(-2)+7=-4+7=3&-(-2)+4=2+4=6\\ -1&2(-1)+7=-2+7=5&-(-1)+4=1+4=5\\ 0&2(0)+7=0+7=7&-(0)+4=0+4=4\\ 1&2(1)+7=2+7=9&-(1)+4=-1+4=3\\ 2&2(2)+7=4+7=11&-(2)+4=-2+4=2\\ 3&2(3)+7=6+7=13&-(3)+4=-3+4=1 \end{tabular}$

From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5.

Therefore, the graph of the two functions will intercect at (1, 5)