Coordinates, slopes and reading a chart
Why this matters
Every chart in this course is points placed on two axes: a loss curve falling as a model trains, a scatter of customers, a line a model fits through data. Reading one well means knowing where each point sits, what the slope of a line says, and how a chart can mislead you. Slope matters far beyond charts, too: "how much does this change when that changes?" is the question behind every rate, every trend and, in Phase 2, every derivative. This lesson builds the skill with numbers first and pictures second.
- Place points on all four sides of zero from their (x, y) coordinates
- Work out a slope as rise over run, and say what its sign and size mean
- Read y = m × x + b as a line, with a slope and a starting value
- Read a chart critically: axes, units, where the axis starts, and how far a trend can be stretched
Two numbers place a point
A chart has two number lines that cross at zero. The across one is the x-axis and the up-and-down one is the y-axis; where they cross is the origin, (0, 0). Any point is two numbers in a fixed order, (x, y): first how far across, then how far up. The order matters: (2, 5) and (5, 2) are different points. A map works the same way, with longitude across and latitude up, and mixing them up puts a store in the wrong country.
Negative numbers carry on past zero, just as on the number line: negative x is left of the origin and negative y is below it. The axes split the page into four regions, called quadrants:
| blank | x is positive | x is negative |
|---|---|---|
| y is positive | top right: (3, 2) | top left: (−3, 2) |
| y is negative | bottom right: (3, −2) | bottom left: (−3, −2) |
In Python, a point is often kept as a pair of numbers in brackets, (3, -2), and a set of points as a list of pairs:
points = [(3, 2), (-3, 2), (3, -2), (-3, -2)] for x, y in points: print("across", x, "and up", y)