Linear Graphs & Coordinate Geometry

Linear Graphs & Coordinate Geometry

1. Linear Functions & their Graphs

   • useful to help see the nature of a function visually rather than working out the algebraic equations
   • x-intercept = value where the line cuts the x-axis
   • y-intercept = value where the line cuts the y-axis

2. Linear Equations by Graphical Method

   • simultaneous equations in two variables x and y --> x + y = 6

3. Length of a Line Segment

   • formula-

4. Gradient of Linear Graphs

   • Lines
     • Horizontal line- m=0
       • y = a, where 'a' is a constant
     • Vertical line- m is undefined
       • x =a, where 'a' is a constant
     • Sloping line with positive gradient- m>0
       • y = mx + c
     • Sloping line with negative gradient- m<0
       • y = mx + c
   • formula-
   • The function of the graphs are straight lines of the form y= mx + c, where 'm' and 'c' are constant. They are called linear equations and the highest power of x in linear equation is 1.
   • When the coefficients of x are parallel, the lines are uphill and slope. When the coefficients of x increases, the stepness of the slopness increase.
   • When the coefficients of x are negative, the lines are downhill and slope. When the coefficients of x are negative, the stepness of the slope increase.

5. Equation of a Straight Line

   • y = mx + c , where 'm' stands for the stepness of the slope and 'c' stands for the y-intercept
   • Lines that are parallel to each other because they have the same gradient; the y-intercept change as the constant term changes