Linear Functions - KidsLearn

The Coordinate Plane

Every point on the grid has an address written as \((x, y)\). The x-coordinate tells you how far left/right, and the y-coordinate tells you how far up/down. The two axes cross at the origin \((0, 0)\), dividing the plane into four quadrants.

Slope-Intercept Form

\(y = mx + b\)

m = slope

How steep the line is. Steeper line → bigger \(|m|\).

b = y-intercept

Where the line crosses the y-axis — the value of \(y\) when \(x = 0\).

Slope = Rise over Run

\(m = \dfrac{\text{rise}}{\text{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}\)

Find the slope through \((1, 2)\) and \((4, 8)\):

\(m = \dfrac{8 - 2}{4 - 1} = \dfrac{6}{3} = 2\)

So the line rises 2 units for every 1 unit it moves right.

Four Kinds of Slope

↗ Positive

Goes up left-to-right (\(m > 0\)).

↘ Negative

Goes down left-to-right (\(m < 0\)).

→ Zero

Flat horizontal line (\(m = 0\)).

↕ Undefined

Vertical line — run is 0, can't divide.

Finding Intercepts

y-intercept: set \(x = 0\) and solve for \(y\). (It's just \(b\).)
x-intercept: set \(y = 0\) and solve for \(x\). For \(y = mx + b\), that's \(x = -b/m\).

📈 Linear Functions