Chapter Review 5: Straight Line Graphs | 第五章复习：直线图

📚 Chapter Review 5: Straight Line Graphs | 第五章复习：直线图

This revision guide covers the key ideas in Edexcel A-Level Pure Mathematics Chapter Review 5: straight line graphs. You will revise gradient, midpoint, distance, equations of lines, parallel and perpendicular conditions, intersections, and modelling.

本复习指南涵盖 Edexcel A-Level 纯数学第五章复习：直线图。你将复习斜率、中点、距离、直线方程、平行与垂直条件、交点以及建模。

1. Gradient and Midpoint | 斜率与中点

The gradient of a straight line joining two points is found by dividing the change in y by the change in x. Always subtract the coordinates in the same order.

连接两点的直线斜率用 y 的变化量除以 x 的变化量来计算。两个坐标必须按相同顺序相减。

m = (y₂ − y₁) / (x₂ − x₁)

The midpoint is the point exactly halfway between the two endpoints. Its coordinates are the average of the x-coordinates and the average of the y-coordinates.

中点位于两个端点正中间。它的坐标是 x 坐标的平均值和 y 坐标的平均值。

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

A positive gradient rises from left to right, while a negative gradient falls. Zero gradient gives a horizontal line, and a vertical line has undefined gradient.

正斜率从左到右上升，负斜率从左到右下降。斜率为零时直线水平，垂直直线的斜率无定义。

2. Equation of a Straight Line | 直线方程

The equation y = mx + c uses m for gradient and c for the y-intercept, which is the point where the line crosses the y-axis.

方程 y = mx + c 中 m 表示斜率，c 表示 y 轴截距，即直线与 y 轴相交的点。

y = mx + c

When you know one point and the gradient, use the point-gradient form y − y₁ = m(x − x₁). You can then rearrange it into the required form.

当已知一个点和斜率时，使用点斜式 y − y₁ = m(x − x₁)。然后可以整理成题目要求的形式。

y − y₁ = m(x − x₁)

To find the equation when given two points, first find the gradient, then

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