Points, Lines, and Planes

Pre-Algebra · Axiom Academy

LESSON Points, Lines, and Planes Two numbers pin down any point on the plane — and a single equation pins down a whole line of them at once. The plane is built from two number lines crossing at right angles. Their meeting point, (0,0) , is the origin . To find a point, read its ordered pair (x, y) as travel directions from the origin: go across by x , then up by y . x-axis — the horizontal number line (left is negative, right is positive) y-axis — the vertical number line (down is negative, up is positive) origin — where the axes cross, the point (0,0) A linear equation is a rule linking x and y . Feed it an x , it hands back a y — and that pair is a point. Take y = 2x + 1 and work out a few: 3. Slope and Intercept Steer the Line Write a line as y = mx + b and the two letters describe its shape directly: b is the height where it crosses the y -axis, and m is its steepness — how much y climbs each time x moves right by one. The line crosses the y -axis at (0, 1) — that's the constant term. Right 1 , up 2 . The same step works anywhere on the line. Slides the whole line straight up or down — same tilt, new crossing point. Tilts the line: bigger m is steeper, negative m slopes downhill, m = 0 is flat. You've seen the plane locate a point, an equation build a whole line of points, and the slope and intercept steer that line. Scroll up to revisit any step.

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