L4 · Graphing a table of values
“I can graph a table of values as points on a coordinate grid, recognize that a linear relation's points lie on a straight line, and use the line to predict values I didn't calculate.”
Table for y = 2x + 1: x = 0, 1, 2, 3 with y = 1, 3, 5, 7. Step 1: Turn each row into an ordered pair: (0, 1), (1, 3), (2, 5), (3, 7). Step 2: Plot them on a grid with x across (0 to 4) and y up (0 to 8): from the origin, go across 0 and up 1 for the first point; across 1, up 3 for the second; across 2, up 5; across 3, up 7. Step 3: Look at the four points: they lie exactly on one straight line. That is not a coincidence - it is what "linear" looks like. The constant difference in the table (+2 per step) becomes the steady climb of the line. Step 4: Use the line: extend it to x = 4 and read off y = 9 - the same value the relation gives (2(4) + 1 = 9), found without a calculation. Say it plainly: table, graph and relation are three views of one pattern. The graph is the fastest view for predicting.
Why do the points of a linear relation always line up straight?
The table for y = x + 4 at x = 1, 2, 3 gives y = 5, 6, 7. Write the ordered pairs and say whether they lie on a straight line. -> (1, 5), (2, 6), (3, 7) - yes, they lie on a straight line (constant difference 1).
"Points (0, 0), (1, 4), (2, ___) lie on one straight line with constant difference 4. The missing output is" -> 8
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.