Today is rung 7 of 22 on this topic
Linear functions and what slope actually means
Can do: Moves between table, graph, equation and words, and interprets slope and intercept in context.
Why it matters
It's the central object of the year and of Algebra I. Slope as rate of change is what makes every later application readable.
What it looks like when it's wobbly
Calculates slope correctly but cannot say what it means; confuses the intercept with the slope in a word problem.
⏱️ Two-minute check
"A taxi charges $3 plus $2 per mile. Write the equation. What does each number mean? Graph it."
Solid looks like: y = 2x + 3, both numbers interpreted in the situation, and a correct graph.
The full activity for this topic · 25 minutes
Four Representations
- 1Take a real linear situation and build a table of values.
- 2Graph it, then write the equation, then describe it in a sentence.
- 3Point at the slope on the graph, in the table, and in the equation — the same number, three places.
- 4Say the slope as a sentence with units: "for every extra mile, $2 more."
- 5Change the starting fee and watch only the intercept move.
If it's too hard
Positive whole-number slopes from a table.
If it's too easy
Negative and fractional slopes, and comparing two plans to find where one becomes better.
Say this
"Say the slope as a sentence with units. Two what, per what?"