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