Thursday
Thursday: The Head-Start Race
Raven opens the Puzzle Post log. "The driveway race. Rocket walked 3 meters every second from the start line."
"And you started 4 meters ahead," Rocket says, "walking 2 meters a second. I still think I won."
"What do you notice at 2 seconds?" Raven asks. "You were at 6. I was at 8."
Rocket checks the log. "At 4 seconds I was at 12 and you were at 12. Then I passed you."
Nova hovers over the two lines on the graph. "Two slopes, two starts," she says. "Write each line."
"Mine is d = 3t," Rocket says. "Raven's is d = 2t + 4. The 4 is her head start."
Nova hums. "The head start is where her line meets the axis. The slope is how fast it climbs."
Slope and y-intercept in a race
Rocket: d = 3t. Slope 3, so 3 meters every second. His line passes through (0, 0): no head start.
Raven: d = 2t + 4. Slope 2, so 2 meters every second. Her line crosses the d-axis at 4, her head start.
A smaller slope with a bigger start: Raven leads early, and Rocket catches up because his line is steeper.
These are the crew's own timings from the driveway race, written in Raven's log. They are made-up Puzzle Post numbers.
| Seconds t | Rocket, meters (3t) | Raven, meters (2t + 4) |
|---|---|---|
| 0 | 0 | 4 |
| 2 | 6 | 8 |
| 4 | 12 | 12 |
| 6 | 18 | 16 |
| 8 | 24 | 20 |
Read a slope from two rows of a table. Raven from (2, 8) to (6, 16): run 4, rise 8, slope 2.
Read a y-intercept from the t = 0 row: Raven has 4 meters at 0 seconds, so b = 4.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
| Statement | True or false? |
|---|---|
| Raven's head start is the y-intercept of her line. | ? |
| The steeper line belongs to the slower walker. | ? |
| Rocket's line passes through (0, 0). | ? |
| In d = 2t + 4, the slope is 4. | ? |
The other starts at the line and takes 2 steps a second. Count seconds together. When do they meet?
Slope and start, read from a log. Tomorrow you find slopes all over everyday life and review the week.