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

Answer: A table of data for two different linear functions using the same values of x for both functions is shown below: x | y=2x+7 y=-x+4 -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 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)

Explanation:

Answer 2

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


`\begin{tabular} 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)