Linear Relationships Flashcards
Linear Graphs
A linear graph is represented by the equation y = mx + b
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Gradient
The gradient m measures how steep a straight line is.
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Intercepts of a Linear Graph
The intercepts are the points where the line crosses the x and y axes.
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Horizontal & Vertical Lines
Horizontal lines have equations x = c and vertical lines have equations y = b.
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Sketching Linear Graphs Using y = mx + b
A straight line graph can be sketched after identifying its y-intercept and gradient.
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Sketching Linear Graphs Using Intercepts
A straight line graph can be sketched after identifying its x-intercept and y-intercept.
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Tables of Values & Linear Rules
The rule for a linear relationship can be found from its Table of Values
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Linear Rule from a Graph
The rule for a linear relationship can be found from its graph.
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[1] Find the y-intercept (b)
[2] Find the rise and the run to determine the gradient (m)
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Linear Rule from Two Points
A variety of questions require you to find the equation of a linear graph given just two points.
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Midpoint of an Interval
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Distance Between Two Points
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Parallel Lines
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Parallel lines have the same gradient.
m1 = m2
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Perpendicular Lines
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Two lines are perpendicular is the product of their gradients equals -1.
m1 × m2 = -1
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Inequalities and Regions
A linear inequality like 2x + y - 2 < 0 represents a region of points in the number plane.
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Distance Formula (5.3)
Point Gradient Formula (5.3)
Direct Variation (Proportion)