Linear Equations
A Linear equation is an algebraic equation that involves constant terms, coefficients and variables.
Linear equation can have one, two or more variables. When it involves only one variable then it is called simple linear equation. For example, 3x=6.
When a linear equation involves two variable with first order it is graphed as a straight line.
First order Linear equation means that variables has maximum degree of 1.
In IB Math AA syllables Linear Equations seen at
IB Math SL AA Topic 2 Linear Equations and their graphs
IB Math HL AA Topic 2 Linear Equations and their graphs
IB Math SL AA Topic 2 Functions – Linear Functions
IB Math HL AA Topic 2 Functions – Linear Functions
IB Math HL AA Topic 5 Derivative – Tangent and Normal Line Equations
Line equation has to common forms:
Slope-Intercept form y=mx+n
In this form of linear equation m is slope and c is the y-intercept
Standard from ax+by=c
In this form of linear equation a,b and c are constants. Slope is given by -a/b.
A line graph defines the relationship between variables, mostly x and y. Slope indicates the change in variable y with respect to one unit change in variable x. In a linear equation y-intercept is the point where the line crosses the y-axis. In a linear equation x-intercept is the point where the line crosses x-axis.
Slope/gradient can be found by formula.
Slope/gradient equals to tangent value of the angle between line and x-axis in positive direction.
To write a line equation one needs slope/gradient (m) and one point (x1, y1) or two points. Line equation can be written as
These formulae are given in IB Math SL DataBooklet. (data booklet a link verebiliriz)
Topic 2.1 Linear Equations and Their Graphs - Equation of a straight line
Topic 2.1 Linear Equations and Their Graphs - Gradient formula
To solve a linear equation in one variable we attempt to find a specific input x that will make the equation true. We can do reverse operations to both sides of the equation.
Two or more linear equation of the first order makes a system of linear equations.
2x+3y =12 and 4x-y=16
System of linear equations can be solved by elimination method or substitution method. These are also called simultaneous solving.
A system of linear equation represents two lines. These two lines can be coincident, parallel or intersect at a single point.
Let system of linear equation be like
ax+by=c and dx+ey=f
If a/d=b/e=c/f then these two lines are coincident
If a/d=b/e but not equal to c/f then these two lines are parallel.
If a/d is not equal to b/e then these two lines intersect at a single point.
From prior knowledge of cartesian system IB Math SL asks distance between two points, midpoint of two points, perpendicular bisector in unit Linear equations and their graphs.
EduIB Questionbank gives you opportunity to solve real past paper like questions about Linear Equations and Their Graphs. (sorulara link verebiliriz)
For example one of Linear Equations and Their Graphs in EduIB is shown below. It is very similar to IB Math SL Exam in May 2023.
