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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