Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

Grade 10 › C10U07 Linear Relations & Functions › L5
GRADE 10 · ALBERTAOUTCOME RF4

L5 · Representing a Linear Relation: Words, Pairs, Tables, Graphs, Equations

Learning goal

“I can name the independent and dependent variables in a context, test whether a relation is linear from a table, a set of pairs, a graph description, or an equation, and convert one linear relation among all five representations.”

Independent variable — the input quantity; the one that is chosen or that drives the situation (plotted on the horizontal axis).
Dependent variable — the output quantity; its value depends on the independent variable (plotted on the vertical axis).
Linear relation — a relation whose graph is a straight line; equivalently, one with a constant rate of change.
Constant rate of change — equal steps in the input always produce equal steps in the output (constant first differences in a table).
Worked example

A gym charges a $40 sign-up fee plus $15 per month. Words: total cost depends on the number of months. Independent variable: months (m). Dependent variable: total cost (C) - it depends on m. Equation: C = 15m + 40. Table: m = 0, 1, 2, 3 -> C = 40, 55, 70, 85. Ordered pairs: (0, 40), (1, 55), (2, 70), (3, 85). Graph: a straight line through those points, starting at (0, 40) and climbing 15 per step. The five views are the SAME relation. In the table, first differences are constant (55 - 40 = 15, 70 - 55 = 15, 85 - 70 = 15) - that constant difference IS the slope, and it is what makes the relation linear.

Check yourself — explain it

The dependent variable is the cost because...

Paired problem — example still visible

A relation is given by the pairs (0, 5), (1, 8), (2, 11), (3, 14). Write its equation. -> First differences are 3, and at x = 0 the value is 5: y = 3x + 5

Faded completion — last step is yours

"Words: 'start at 90, decrease by 6 each step.' Table first row x = 0: y = ___; the equation is y = ___." -> 90; y = -6x + 90

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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