Linear Equations And Functions

Linear Equations And Functions

1. Introduction

   • A Linear Equation is an equation for a straight line
     • e.g.: ax+by=c
     • Linear Function
       • Y=F(x)=ax+b

2. Intercepts and Slope

   • x-intercept and y-intercept can be found by setting x/y=0
   • slope:

3. Finding the Equation of a Line

   • Two-Point Form
     • m1=m2
       • y-y1/x-x1 = y2-y1/x2-x1
   • Point-Slope Form
     • When the line has slope & passes through point (x,y)
       • y-y0=m(x-x0)
   • Slope Intercept Form
     • When given point (0,y) and slope m:
       • y-b = m(x-0) , y= mx+b

4. Intersection of Straight Line

   • finding the point of intersection of two straight line

5. Parallel and perpendicular Line

   • Perpendicular Lines Two lines are Perpendicular if they meet at a right angle (90°). How do we know if two lines are perpendicular? When we multiply their slopes, we get −1
     • m1 = −1/m2 m2 = −1/m1
     • m1m2 = −1
   • Parallel Lines . Their slopes are the same!
     • The slope is the equation of a line: y = mx + b

6. Piecewise Linear Function

   • Is a Function that defined by more then one rule.
     • Example: Here is another piecewise function:

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