unit 1 – first-degree equations and inequalities chapter 2 – linear relations and functions 2.2...
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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