Slope & intercept

Japanese school year: Junior high 2

What you learn

You will explore how the slope and y-intercept determine the behavior and position of a straight line on a graph. This concept is widely used to visualize and model steady rates of increase or decrease in data. Prior knowledge of direct proportions and plotting coordinates will support your understanding.

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Key points

This is the standard form of a linear function. The constant $a$ represents the slope (rate of change) of the line, and $b$ represents the $y$ -intercept where the line crosses the $y$ -axis.

y = ax + b

This formula calculates the slope $a$ (rate of change) of a line passing through two distinct points. It is found by dividing the change in $y$ by the change in $x$ .

\frac{y_2 - y_1}{x_2 - x_1} = a \quad (x_1 \neq x_2)

This relationship identifies the intersection of the line with the $y$ -axis. Substituting $x = 0$ yields $y = b$ , showing that the line crosses the $y$ -axis at $(0, b)$ .

x = 0 \implies y = b

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Practice 1Coming soon