Finding and interpreting the intersection of two linear graphs

Task goals

• Complete a table of values for a linear rule such as y = 2x + 1, choosing or using given x-values.
• Plot the points from two tables of values on the same grid and join each set with a straight line.
• Locate where the two lines cross and write the point of intersection as an ordered pair (x, y).
• Explain what the point of intersection means: at that point both relationships have the same x-value and the same y-value.
• Interpret the x- and y-coordinates of the intersection in a real context, and use the graph to say which relationship is greater before the crossing and which is greater after it.
• Extension: find the intersection algebraically by equating the two rules, solving for x, and substituting back to find y.