Unit 1 – First-Degree Equations and Inequalities

Chapter 2 – Linear Relations and Functions2.2 – Linear Equations

2.2 – Linear Equations• In this section we will review how

to:– Identify linear equations and

functions

– Write linear equations in standard form and graph them

2.2 – Linear Equations

• Linear equation – no other operations other than addition, subtraction, and multiplication of a variable by a constant– x + y = 4– variables cannot be multiplied together– variables cannot appear in a denominator– variables cannot have exponents higher

than 1– graph is always a line

2.2 – Linear EquationsLinear Equations• 5x – 3y = 7• x = 9• 6s = -3t – 15 • y = 1/2x

Not Linear Equations• 7a + 4b2 = -8• y = √(x + 5)• x + xy = 1• y = 1/x

2.2 – Linear Equations

• Linear function – function whose ordered pairs satisfy a linear equation– f(x) = mx + b where m and b are real

numbers

2.2 – Linear Equations

• Example 1– State whether each function is a

linear function. Explain• g(x) = 2x – 5

• p(x) = x3 + 2

• t(x) = 4 + 7x

2.2 – Linear Equations

• Example 2– The linear function f(C) = 1.8C + 32 can be used to

find the number of degrees Fahrenheit f(C) that are equivalent to a given number of degrees Celsius C.

• On the Celsius scale, normal body temperature is 37°C. What is it in degrees Fahrenheit?

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

2.2 – Linear Equations

• Standard Form– Ax + By = C

• A, B and C are integers whose greatest common factor is 1

• A ≥ 0• A and B are not both zero

2.2 – Linear Equations

• Example 3– Write each equation in standard form.

Identify A, B and C.• y = 3x – 9

• -⅔x = 2y – 1

2.2 – Linear Equations

• How many points determine a line?

• y – intercept – The y-coordinate of the point at which a graph crosses the y-axis

• x – intercept – The x-coordinate of the point at which a graph crosses the x-axis

2.2 – Linear Equations

• Example 4– Find the x-intercept and the y-

intercept of the graph of -2x + y – 4 = 0. Then graph the equation.

2.2 – Linear Equations

HOMEWORKPage 69

#11 – 17 odd, 18 – 21 all, 23 – 47 odd