Grade 8: Linear Functions

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Objective - To graph linear equations using the slope and y-intercept.

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Presentation transcript:

Grade 8: Linear Functions Writing Linear Equations from a Description to Represent Real- World Scenarios Key Vocabulary: Independent & Dependent Variables Initial Value (y-intercept) Slope & Rate of Change

OBJECTIVE: Be able to write a linear equation (function rule) from a description in a real-world situation by identifying the input (independent) & output (dependent) variables and determining the rate of change (slope) and y-intercept (initial value.)

WARM UP Determine the slope using two ordered pairs: (4,7) (7,13) (4,5) (8,4)

REVIEW Writing an equation from a graph. Page 308

EXPLORE Page 309

Steps: Identify the Input & Output Variables: The ___________________________________________ is a function of _______________________________________. Write the information (input, output) as ordered pairs. At 59° F, crickets chirp 76 times per minute ( , ) At 65° F, crickets chirp 100 times per minute ( , )

Steps: 3. Calculate the Slope (rate of change) m Use Slope Intercept Form Equation y = mx + b and one of the ordered pairs from the description: and substitute the y-value, slope and x-value into the equation; then solve for the y-intercept (b). 5. Write the equation in the y = mx + b form, substituting for the slope m and the y-intercept b. y = 4x - 160

Use Function Rule to Predict: y = 4x – 160 Predict the number of chirps when the temperature is 72° F. Will the graph “rise” or “ fall” from left to right? What does the sign of the slope mean in this context?

PRACTICE Complete the practice problems on worksheet page 310 For each scenario, be able to answer the following questions: What are the input ant output variables? ________________ is a function of _____________________. What is the “initial value” and what does it mean? Will the graph of this function “rise” or “fall” ? What does the slope mean?

EXIT Ticket John is tracking Garfield’s weight and he has noticed that after Garfield ate 2 lasagnas he weighed 35 pounds and after he ate 4 lasagnas he weighed 39 pounds. Identify the independent & dependent variables and complete the statement: _________________________is a function of _________________________. Write the ordered pairs: _________ _________ Determine the slope and y-intercept and write the linear equation that represents Garfield’s weight as a function of the number of lasagnas he eats. What does the y-intercept represent?