Aim: How can we identify linear functions and write linear equations

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Presentation transcript:

Aim: How can we identify linear functions and write linear equations Aim: How can we identify linear functions and write linear equations? Do Now: Given f(x)=4x2+9, find f(-2) and f(4y)

Homework ???s

linear relations – relations that have straight line graphs. linear equation – has no operations other than addition, subtraction, and multiplication of a variable by a constant. linear function – a function with an ordered pair that satisfy a linear equation. Vocabulary

X-intercept : point where graph crosses x-axis (x,0) Y-intercept : point where graph crosses y-axis (0,y) Vocabulary

Linear Equations: Nonlinear Equations: 4x-5y=16 2x + 6y2=-25 x=10 (vertical line) y=√x + 2 y=-4 (horizontal line) x + xy = -5/8 f(x)=-2/3x – 1 f(x) = 1/x y=0.5x xy = 12 Vocabulary

Identify Linear Functions A. State whether g(x) = 2x – 5 is a linear function. Write yes or no. Explain. Answer: Yes; this is a linear function because it is in the form g(x) = mx + b; m = 2, b = –5. Example 1A

Identify Linear Functions B. State whether p(x) = x3 + 2 is a linear function. Write yes or no. Explain. Answer: No; this is not a linear function because x has an exponent other than 1. Example 1B

Is xy = 3 a linear function. Explain. B C D Example 1C

Is 1 + 1 = 3 a linear function. Explain. x y B C D Example 1C

Is f(x) = √3-x a linear function. Explain. B C D Example 1C

f(C) = 1.8C + 32 Original function f(37) = 1.8(37) + 32 Substitute. Evaluate a Linear Function A. METEOROLOGY 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? f(C) = 1.8C + 32 Original function f(37) = 1.8(37) + 32 Substitute. = 98.6 Simplify. Answer: Normal body temperature, in degrees Fahrenheit, is 98.6°F. Example 2

A B C D A. 0.6 second B. 1.67 seconds C. 5 seconds D. 15 seconds Example 2B

Concept

Write y = 3x – 9 in standard form. y = 3x – 9 Original equation –3x + y = –9 Subtract 3x from each side. 3x – y = 9 Multiply each side by –1 so that A ≥ 0. Example 3

Write 3x + 6y = – 18 in slope-intercept form. Example 3

Write y - 3 = 4(x + 6) in slope-intercept form. Point -Slope Form Write y - 3 = 4(x + 6) in slope-intercept form. Example 3

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