Grade 6 › U09 Patterns & Functions

Grade 6 › U09 Patterns & Functions › L4
NUMBER · GRADE 6 · ALBERTAOUTCOME AB-MAT6-P1

L4 · Writing an equation for a function

Learning goal

“I can write an equation for a function - like d = 15t - explain what every letter and number in it means, and use the equation to calculate outputs for any input.”

Equation — a statement with an equals sign that gives the dependent value from the independent value, like d = 15t.
Variable — a letter in an equation that stands for a changing quantity. In d = 15t, t stands for the time in hours and d stands for the distance in kilometres.
Function rule — the same rule as before, now written as an equation instead of in words: "multiply by 15" becomes d = 15t.
Substitute — to put a number in place of a letter in an equation and calculate, like putting t = 4 into d = 15t to get d = 60.
Worked example

A bus travels 15 km every hour. The equation is d = 15t, where t is the time in hours (independent) and d is the distance in kilometres (dependent). Step 1: Read the equation in words: "distance equals 15 times the time". The 15 is the number of kilometres travelled in each hour. Step 2: Substitute t = 4: d = 15 x 4 = 60 km. Step 3: Check against the table and the graph: the table row 4 -> 60 and the point (4, 60) say the same thing three ways - words, table, graph, equation all describe one function.

Check yourself — explain it

In the equation C = 6n for the cost of notebooks at $6 each, the letter n is...

Paired problem — example still visible

Each bag of feed has a mass of 4 kg: m = 4b. Find m when b = 7. -> m = 4 x 7 = 28 kg

Faded completion — last step is yours

"P = 9h (pay in dollars for h hours). When h = 5, P = 9 x 5 = ___." -> $45

Ready to practise?

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

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