Linear Relationships (HSC SSCE Mathematics Standard): Flashcards

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Linear Models
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What is a linear model?

Math representation of real-world using straight-line equation

Gradient-intercept form equation

y=mx+by = mx + b

What does mm represent in y=mx+by = mx + b?

Gradient (rate of change)

What does bb represent in y=mx+by = mx + b?

yy-intercept (starting value when x=0x = 0)

Formula to calculate gradient

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} or Rise over Run

What is xx in y=mx+by = mx + b?

Independent variable (value we know or choose)

What is yy in y=mx+by = mx + b?

Dependent variable (value we calculate)

Practical meaning of gradient in linear models

Rate of change, cost per item, speed, or rate of flow

Practical meaning of intercept in linear models

Base fee, initial amount, or starting value

Steps to find equation from a graph

Calculate gradient using two points, identify intercept

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