Download Linear Equations Notes

Algebra II HONORS
Writing Linear Eqns.-Notes
Name _______________________
Date ____________________
Linear Equations- An equation whose graph is a line is a Linear Equation.
Slope-Intercept Form of an Equation
y = mx + b_ m is ___________________ b is _________________________
1) Write the Equation of the line based on the graph:
Y-intercept (b-value)? _________
x
Slope (m-value)? ____________
Equation: y = ____________________
y
Write the equation given the slope and y-intercept (use the form: y=mx+b):
2
2) m = -3, b = 1
3) m   , b  4
5
Write the equation given the slope and a point on the graph:
4) Given: m  1, (2,1)
Steps: 1) Calculate the b-value by substituting the
slope and the coordinates into y=mx+b.
2) Plug the m and b values back in:
y=____x+____
Write the equation given only 2 points on the graph:
5) Given (-1, 3) and (2, 1)
y2  y1
x2  x1
2) Calculate b by substituting the slope (m)
and one of the coordinates into y=mx+b
Steps: 1) Calculate slope (m) using: m 
3) Plug the m and b values back in:
y=____x+____
Standard Form is Ax  By  C where A, B, and C are integers, A&B are not both zero, and A  0 .
Why??
Determine whether or not each is a linear equation:
1) 5 x  3 y  7
* 4) y  x  5
2) x  9
5) 6s  3t 15
* 3) 7 a  4b 2  8
* degree cannot be other than 1
* 6) x  xy  1
Examples: Write each equation in Standard Form such that A,B & C are integers whose GCF is 1. Identify
A,B & C.
1) y  2 x  5
A=
2)
3
2
x  y 3
4
3
B=
C=
3) 3x  9 y  27
A=
B=
C=
4) y  x  2
A=
B=
C=
A=
B=
C=
Definition of a Linear Function: A function is linear if it can be defined by f ( x)  mx  b , where m and b
are Real numbers (recall this is slope-intercept form).
m = slope
b = y-intercept
If m = 0, f ( x)  b (graph is a horizontal line) - a constant function.
If f ( x)  0 , it is called the zero function. (What is its graph? __________________ )
Determine whether or not each function listed below is a linear function,
and name m and b:
f ( x)  3x  2
g ( x)  x 2  7
h( x )  5  6 x
The y-value where the graph crosses the y-axis is the _________________ (x-coord = )
The x-value where the graph crosses the x-axis is the _________________ (y-coord = )
Graph using x & y-intercepts (good way to graph with equations in Standard Form)
6 x  2 y  12
10 x  y  10
y
y
x
x
Due Tomorrow A.12
AND
“What Do Man-Eating Fish…” WS
AND
“What Did the Electrician…” WS