Algebra
Lesson 4-5
Vocabulary:
Linear Equation: An equation in the form Ax + By = C, whose graph is a straight line.
Standard Form: The standard form of a linear equation is Ax + By = c, where A > 0, and A and B are not both zero.
X-Intercept: The coordinate at which a graph intersects the x-axis.
Y-Intercept: The coordinate at which a graph intersects the y-axis.
Examples:
Identify Linear Equations
a. y = 5 - 2x
y + 2x = 5 - 2x + 2x
2x + y = 5
The equation is now in standard form where A=2, B=1, and C+5. This is a linear equation.
b. 2xy - 5y = 6y
Since the term 2xy has two variables, the equation cannot be written in the form Ax + By = C. Therefore,
this is not a linear equation.
c. 3x + 9y = 15
Since the GCF of 3, 9, and 15 is not 1, the equation is not written in standard form. Divide each side by the GCF.
3x + 9y = 15
3(x + 3y) = 15
3(x + 3y) = 1515
3 3
x+ 3y = 5
The equation is now in standard form where A = 1, B = 3, and C = 5.
d. 1/3y = -1
To write the equation with integer coefficients, multiply each term by 3.
3(1/3)y = 3(-1)
y = -3
Graph by Making a Table
Graph x + 2y = 6.
In order to find values for y more easily, solve the equation for y.
x + 2y = 6
x + 2y - x = 6 - x
2y = 6 - x
2y = 6 - x
2 2
y = 3 - 1/2 x
Select five values for the domain and make a table. Then graph the ordered pairs.
Make a table before you graph.
Additional Information:
A linear equation cannot have more than two variables , no powers bigger than
one and numbers in the equation cannot be multiplied by each other. A standard
equation cannot have fractions, it must be simplified. A standard equation
is in the form of Ax + By = C. A standard equation must have two or less
variables also.
Online resources: http://www.studygs.net/equations.htm
Pictures:
This page by: AS, DRV, EV