Linear Models (HSC SSCE Mathematics Standard): Quizzes

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Linear Models
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In the form y=mx+by = mx + b, what does mm represent in a linear model?

The gradient (rate of change)

What does the yy-intercept (bb) represent in a linear model?

The starting value when x=0x = 0

A catering company uses c=25n+100c = 25n + 100. What does the gradient 25 represent?

Cost per guest

In c=25n+100c = 25n + 100, what does the intercept 100 represent?

Base fee of 100 dollars

Which formula calculates the gradient between points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)?

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

In a water tank model V=100t+400V = 100t + 400, what was the initial volume of water?

400 L

For V=100t+400V = 100t + 400, what does the gradient 100 represent?

Pumping rate of 100 L/min

What are linear models particularly useful for representing?

Constant rates of change

In practical situations, what can the gradient of a linear model represent?

A cost per item or rate of flow

When reading values from a linear graph, what technique should you use?

Trace horizontal and vertical lines

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