What is the standard form of a linear function? - y = mx + b, What is the commutative property form of a linear equation often used in the tank problems? - y = b + mx, How can you tell if a linear function is increasing from its equation? - The rate of change or slope is positive, How can you tell if a linear function is decreasing from its equation? - The rate of change or slope is negative, How can you tell if the initial value of a function is positive from a graph? - The graph crosses the vertical axis above the origin, What does the initial value represent in an equation? - It is the constant term or b value, Jada earns $7 per hour mowing lawns. Name the two quantities in this functional relationship. - Hours worked and money earned, In Jada's job scenario, which quantity is typically the independent variable? - Hours worked, Write an equation representing Jada's earnings E as a function of hours worked h. - E = 7h, To convert feet to yards, you multiply the number of feet by one-third. Which is the independent variable? - Number of feet, Write an equation to convert feet f to yards y. - y = (1/3)f, If feet f is a function of yards y, what is the equation? - f = 3y, Amount of water A in Tank A is A = 200 + 8t. Is it filling up or draining out? - Filling up, Why is Tank A filling up? - Because the rate of change (+8) is positive., Tank B starts at 400 gallons and decreases at 5 gallons per minute. Write its equation. - B = 400 - 5t, Tank A (A=200+8t) and Tank B (B=400-5t), which tank started with more water? - Tank B, Between Tank A (A=200+8t) and Tank B (B=400-5t), which tank started with more water? - Draining out, How can you tell Tank C is draining just by looking at the equation? - The slope or rate of change is negative (-7), If Tank D's graph is a line sloping downward toward the t-axis, is it filling or draining? - Draining out, Elena's savings account equation is E = 8w + 60. What is her weekly saving rate? - $8 per week, Based on Noah's graph, how much money did he have in his account at 0 weeks? - $60, Between Noah (starting at $60) and Elena (E = 8w + 60), who started with more money? - They started with the same amount, Noah's graph shows $70 at 2 weeks and $80 at 4 weeks. What is his saving rate? - $5 per week, Who is saving money at a faster rate, Noah ($5/wk) or Elena ($8/wk)? - Elena, How many weeks are typically considered for a year in these saving problems? - 52 weeks, How would you calculate Noah's savings after one year? - Start amount + (rate times 52), If Noah saves $5 a week starting with $60, what is his total after 52 weeks? - $320, What equation would solve how long it takes Elena to save a specific target amount T? - T = 8w + 60, If a graph of a function is a straight line, what type of function is it? - A linear function, How does the graph of a linear function relate to its rate of change? - The rate of change determines the steepness and direction of the line.,

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