2.2: Linear Equations
Our greatest glory is not in never falling, but in getting up
every time we do.
Graphing Linear Equations
y  mx  b
• y is called the dependent variable
because the value of y depends on x
• x is called the independent variable
4
Ex1) Graph the equation y   x  2
3
x
4
y  x2
3
5
4
y
(x, y)
3
2
1
-5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
2
3
4
5
Standard Form
Standard form of a linear equation is Ax + By = C, where A, B,
and C are real numbers and A, B ≠ 0.
Graph linear equations in standard form by finding the
x- and y- intercepts
5
Ex2) 2 x  4 y  8
4
3
2
1
-5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
2
3
4
5
More Practice
Ex3) The equation 10x + 5y = 40 models how you
can give $0.40 change if you have only dimes and
nickels. The variable x is the number of dimes, and
y is the number of nickels. Graph the equation.
Describe the domain and the range. Explain what
the x- and y-intercepts represent.
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
Slope
y
vertical change (rise)
y2  y1
slope 


x horizontal change (run)
x2  x1
Ex4)  2, 2  and  4,2 
Ex5)  2,7  and 8, 6 
Slope (cont.)
y (rise)
slope 
x(run)
What does it mean if the slope is zero?
What does it mean if the slope is Undefined?
Point-Slope Form
The line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Ex6) Write in standard form an equation of the line with
1
slope  through the point ( 6,2).
3
Point-Slope Form
The line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Ex7) Find the equation of a line through the points (-2, 3)
and (1, 6). Then write it in standard form.
Slope-Intercept Form
y = mx + b
Ex8) What is the slope of the
line 4x + 6y = 18?
What is the slope of:
a horizontal line?
a vertical line?
parallel lines?
perpendicular lines?
Perpendicular Lines
Ex9) Write an equation of the line through (5, –3) and
perpendicular to y = 4x + 1. Graph both lines.
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6
2.2: Linear Equations
HW: # 1-15 odd,
20 – 36 even, 38-41
Our greatest glory is not in never falling, but in getting up
every time we do.