IB Maths AI 2.1 Definitions

This page contains our IB Maths AI definitions for 2.1. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Forms of lines'.

All Topic 2 Sub-topics 2.1: Forms Of Lines 2.2: Introduction To Functions 2.3: Introduction To Modelling Functions 2.4: Modelling Applications (HL)2.5: Further functions (HL)2.6: Graph transformations (HL)2.7: Advanced modelling functions (HL)2.8: Logarithmic graphs

gradient

The coefficient

a

y=ax+b

, giving the predicted change in

y

when

x

increases by

1

gradient-intercept

A form of a straight-line equation written as

y=mx+c

, where

m

is the gradient and

c

is the

y

-intercept.

Intercepts

The points where a line crosses the coordinate axes; the

y

-intercept occurs when

x=0

and the

x

-intercept occurs when

y=0

parallel

Checks consistency by comparing results from two different versions designed to measure the same thing.

perpendicular

Meeting at a right angle, so the angle between the two lines is

90^{\circ}

point-gradient

A form of a straight-line equation using a point

(x_1,y_1)

and gradient

m

y-y_1=m\left(x-x_1\right)

vertical

Describing changes parallel to the

y

-axis, such as a stretch by factor

|a|

or a shift up or down by

d

x-intercept

The point where a line crosses the

x

-axis, found by setting

y=0

and solving for

x

, giving a point of the form

(x,0)

y-intercept

The point where a line crosses the $y$ -axis, found by setting $x=0$ in the equation of the line.

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