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Algebra 1 9-12 / Week 04 / Friday
5/6
Week 04 · Linear Graphs and Rates of Change

Friday

Lines everywhere
// The cart on the ramp, one second at a time
⏱ about 20 min

Friday: Lines Everywhere

Comet drops onto the Loft couch. "Lines are everywhere now. I timed myself walking home: 80 meters a minute."

"Then your distance is a line, d = 80t," Wren says. "What do you notice about its intercept?"

"Zero. I started at the door." She sits up. "And my phone battery. It fell 2 percent every 10 minutes."

"A falling line, like the jug," Wren says. "Write the rule and read where it reaches zero."

Nova projects a tiny grid with a line sloping down. "Would you like a hint? Minutes across, percent up."

"Start at 100, down 0.2 a minute, so 100 - 0.2t. Zero at 500 minutes," Comet says.

"Review time," Wren says. "Our engineer, five features, every graph. Then next week we build the cup tower."

Lines in a day

  • Walking at a steady pace: distance rises by the same amount each minute. Increasing, intercept at the start.
  • A battery or a jug draining steadily: decreasing, positive until it reaches zero at the horizontal intercept.
  • A kitchen timer counting down: decreasing by 1 each second, reaching zero when it rings.
  • Cups stacked at the same height each: increasing, rate equal to one cup's height.
A grid from 0 to 10 with a rising line for a walk and a falling line for a timer.

The week in five lines

  • A linear function graphs as a straight line. The rate of change is its slope.
  • The y-intercept is the output at input 0. The horizontal intercept is where the output is 0.
  • Positive slope means increasing. Negative slope means decreasing.
  • Graph by hand: axes with labels and a scale, the intercept, one step with the rate, the line.
  • Average rate of change over an interval is change in output over change in input, line or not.
EVERYDAY LINES
  • Read the question.
  • Tap your answer.
Comet walks 80 meters a minute from her door. Which equation is her distance line?
A battery follows p = 100 - 0.2t percent. After how many minutes does it reach zero?
The battery rule is p = 100 - 0.2t. Increasing or decreasing?
Comet's walk is d = 80t meters. How far has she gone after 15 minutes?
MIXED REVIEW
  • Read the question.
  • Tap your answer.
A line passes through (2, 7) and (5, 16). What is its rate of change?
The same line passes through (2, 7) and (5, 16). What is y when x = 0?
For g(x) = x² + 1, what is the average rate of change from x = 1 to x = 3?
The cart rule is f(t) = 3t + 1. What is f(7)?
StatementTrue or false?
A negative rate of change means the graph goes down from left to right.?
The y-intercept of y = 5x - 2 is 5.?
The graph of y = 12 - 2x crosses the horizontal axis at x = 6.?
The average rate of change of a line is the same on every interval.?
The point (2, 160) is on the graph of y = 80t.?
100 - 0.2 × 500 = 0?
WHY THIS EXERCISEThese are the week's key features. Next week you build rules from situations and sequences.
Try it
Time yourself walking a hallway at a steady pace and count your steps each 5 seconds. Graph it with labels and a scale.
Walk, never run, and keep the hallway clear.
Draw Comet's walk and the battery on two small grids. Label axes, scales and both intercepts.

Terrific week. You can read, draw and compare linear graphs. Tomorrow is Loft Day.

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