1-3 Linear Equations and Functions and Lines
Linear equations
equations of form: Ax + By = C
where A, B, C are numbers
its graph will be a straight line
example:
x + 2y = 4
here, A=1, B=2 and C=4. Its graph:
Linear functions
 solving x + 2y = 4 for y, we get: y = -(1/2)x + 4
 the function defined by this equation is (of course):
f(x) = -(1/2)x + 4
 its graph is (of course) the above
 such functions are called linear functions
1-3
p. 1
Forms of the Equation of a Line
1. slope-intercept form: y
=
mx +
b
        
slope
2. point-slope form:
y - y1
=
y-intercept
m(x -
x1)
 
slope

point: (x1, y1)
3. standard form:
Ax + By = C
Six skills
1.
2.
3.
4.
5.
6.
1-3
Given:
Find:
any linear equation
its standard form
method: rearrange using algebra
any linear equation
its slope-intercept form
method: solve for y
two points
slope of line through them
method: slope formula
equation of line
slope of line
method:
put into slope-intercept; inspect result for slope
point and slope
equation of line through given
point with given slope
method: point-slope form
two points
equation of line through them
method: use slope formula to get slope;
point-slope form to get equation
p. 2