This document discusses linear equations and functions. It defines the standard function format as y=ax+b, where a is the slope and b is the y-intercept. It describes properties of lines such as parallel and perpendicular lines. It also discusses how to find the equation of a line given two points, and how to write a linear equation in function format by isolating the y-variable. Finally, it explains how to solve a linear system by finding the point of intersection between two lines.

1. Linear Equations
Math Science Option

2. Function Format
 y = f(x) = ax + b
 Where y is a function of x, y is based
on x.
 ‘a’ is ROC/ slope = Δy = y2-y1
Δx x2-x1
‘b’ is the y intercept or initial value.
E.g. y = 2x + 1
Slope is 2 and the y intercept is 1.

3. Properties
 Lines with the same slope, a, are
parallel.
 Lines with different slopes, a, must
intersect somewhere.
 A positive slope goes up from left to
right.
 A negative slope goes down from left to
right.
 A line perpendicular (at 90°) to a line
with slope ‘a’ has a slope ‘-1/a’.

4. Example
 Given the points, (2,3) and (5,-6),
what is the equation of the line?
 Page 256, Q. 1,2,4,5,6,11

5. Characteristics of Linear Function
Characteristic Basic Fn
Direct
Transformed
Partial
Rule y= 1x y = ax+b
a is #, is y.i.
Domain ]-∞,∞[ ]-∞,∞[
Range ]-∞,∞[ ]-∞,∞[
Extreme none none
Zero of fn x = 0 -b/a
Sign: pos ]0,∞[ Depends
Sign: neg ]-∞,0[ Depends

6. General Format
 Ax + By + C = 0
 This can be turned into the function
format by isolating the y.
 E.g. 4x + 5y + 7 =0
 5y = -4x – 7…we have isolated 5y
 y = -4x/5 – 7/5…we have isolated y
 Therefore, slope is -4/5 and y
intercept is -1/4

7.  Solving a linear system means
finding the (x,y) where 2 lines
intersect.
 Page 262, Q. 1-6

8. Systematic Format
 x + y = 1
a b
 where a is the x intercept and b is
the y intercept.
 E.g. x/2 + y/5 = 1
 Gives us (2,0)… x intercept
 And (0,5)…y intercept.

9. Example
 Express x/2 + y/5 = 1 in function
format.
 Multiply by 10 (5x2) to get rid of the
fractions on both sides.
 This gives 5x + 2y = 10
 Isolate the 2y…2y = -5x + 10
 Isolate the y….y = -5/2 x + 10/2
 y = -2.5x + 5

10. Activity
 P. 271, Q. 27
 P. 273, Q. 1,2