2-2 Linear Equations

•We will identify linear equations and functions.

Linear Equations A linear equation has no operations other

than addition, subtraction, and multiplication of a variable by a constant.

The variables cannot be multiplied together or appear in the denominator.

Variables cannot have exponents other than 1.

And the graph of a linear equation is always a line.

Equations Linear Equations

5x – 3y = 7

x = 9

6s = -3t – 15

y = ½ x

Not Linear Equations

7a + 4b2 = -8

y = x + 5

x + xy = 1

y = 1/x

Linear Functions

A linear function is a function that can be written in the form f(x) = mx + b, where m and b are real numbers.

Ex.1 State whether each function is a linear function. Explain.

a) g(x) = 2x – 5

b) p(x) = x3 + 2

c) t(x) = 4 + 7x

Ex. 2 The linear function f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit, f, that are equivalent to a given number of degrees Celsius, C.

a) On the Celsius scale, normal body temperature is 37 degrees. What is the normal body temperature in degrees Fahrenheit?

h

Ex. 2 The linear functions f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit, f, that are equivalent to a given number of degrees Celsius, C.

a) On the Celsius scale, normal body temperature is 37 degrees. What is the normal body temperature in degrees Fahrenheit?

f(37)=1.8(37) + 32 =98.6 OF

h

Ex. 2 The linear functions f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit, f, that are equivalent to a given number of degrees Celsius, C.

b) There are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees between these two points. How many Fahrenheit degrees equals 1 Celsius degree?

h

Ex. 2 The linear functions f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit, f, that are equivalent to a given number of degrees Celsius, C.

b) There are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees between these two points. How many Fahrenheit degrees equals 1 Celsius degree?

If 100OC = 180OF…then 1OC = 1.8OF

h

In lesson 2-1, we graphed an equation by making a chart of values and then graphing and connecting the ordered pairs.

Since 2 points determine a line, one way to graph a linear equation or function in to determine where it will cross each axis and then connect those points. (Find the intercepts.)