Final answer:
To answer the student's question, create a table by selecting various x values and computing the corresponding y values using the equation y = 2x + 6. Then plot these points on a coordinate graph and draw a straight line through them to visualize the linear relationship.
Step-by-step explanation:
To create a table and a graph for the algebraic rule y = 2x + 6, start by choosing several different values for x. Next, calculate the corresponding y values using the equation. Here's an example of how to construct the table:
- If x = -2, then y = 2(-2) + 6 = 2.
- If x = 0, then y = 2(0) + 6 = 6.
- If x = 1, then y = 2(1) + 6 = 8.
- If x = 2, then y = 2(2) + 6 = 10.
- If x = 3, then y = 2(3) + 6 = 12.
Once you have a set of (x,y) points, plot them on a graph with the x-axis horizontal and the y-axis vertical. After plotting the points, draw a straight line through them to represent the equation y = 2x + 6. This line will have a slope (rise over run) of 2, meaning it goes up 2 units for every 1 unit it goes to the right, and it crosses the y-axis at (0,6).