A2. Linear Relationships Flashcards by Ian Gillies

Q

Linear Functions

The equation y = mx + c represents a linear function.

m =
c =

A

The graph of a linear function is a straight line.

m = the gradient of the line.
c = y-intercept

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Q

Positive and Negative Gradient

Gradient can be positive or negative.

A

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Q

Gradient Formula

The gradient m measures how steep a straight line is.

A

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Q

Finding the Gradient

If you have two points that the line passes through …

A

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Q

Intercepts of a Linear Graph

The intercepts are the points where the line crosses the x and y axes.

A

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Q

Graphing a Linear Function

A linear function can be graphed using its y-intercept and gradient.

A

[1] Plot the y-intercept on the y-axis.

[2]Use the rise and the run of the gradient to plot the next points on the graph.

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Q

Tables of Values & Linear Rules

The rule for a linear relationship can be found from its Table of Values.

A

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Q

Linear Rule from a Table of Values 2

The x-values of some tables of values are not equally spaced.

A

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Q

Linear Rule from Two Points

A variety of questions require you to find the equation of a linear graph given just two points.

A

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Q

Linear Models

A linear model is a mathematical formula that represents the relationship between two variables.

A

A linear model of Depreciation

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Q

Linear Models and Variables

Every linear model has a dependent and an independent variable.

A

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Q

Linear Models and Gradient

To determine what the gradient of a linear model represents, include the units of the two variables when working out the rise over run.

A

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Q

Linear Models and the Vertical Intercept

The vertical intercept (y-intercept) represents the starting value of the dependant variable.

A

The PC was worth $2000 when purchased.

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Q

Direct Linear Variation

In direct linear variation, two quantities, such as time & wages, increase at a constant rate.

A

For each increase in time of 1 hour, wages increase by $25.

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Q

The Direct Linear Variation Equation

The equation that describes direct linear variation is y = kx

A

y = kx graphs are linear graphs which start at the origin

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Q

Constant of Variation

k is called the constant of variation (or constant of proprotionality)

A

You will usually have to find the value of k at the start of a question (even if the question does not ask you to).

Q

Conversion Graphs

A conversion graph is used to convert between different units (eg metric and imperial units) or between different currencies.

A

Conversion graphs are another example of the equation y = mx.

Q

Linear Variation Problems

A