Straight Line Graphs: Gradient, Equation and Intercepts | 直线图像：斜率、方程与截距

📚 Straight Line Graphs: Gradient, Equation and Intercepts | 直线图像：斜率、方程与截距

In IGCSE Mathematics, straight line graphs form a bridge between algebra and geometry. They appear in coordinate geometry, functions, sequences and real-life contexts. Understanding gradient, intercepts and the equation y = mx + c allows you to plot lines, find equations from conditions, and solve problems involving parallel or perpendicular lines.

在 IGCSE 数学中，直线图像是代数与几何之间的桥梁。它出现在坐标几何、函数、数列以及实际生活情境中。理解斜率、截距和方程 y = mx + c，能够帮助你绘制直线、根据条件求方程，并解决平行线或垂直线问题。

1. The Coordinate Plane and Plotting Points | 坐标平面与描点

The coordinate plane is formed by two perpendicular number lines. The horizontal line is the x-axis, the vertical line is the y-axis, and they meet at the origin, written as (0, 0).

坐标平面由两条互相垂直的数轴组成。水平线叫 x 轴，垂直线叫 y 轴，它们的交点叫原点，记作 (0, 0)。

A point is located by an ordered pair (x, y). The first number is the horizontal distance from the origin, and the second number is the vertical distance. For example, the point (−3, 2) lies 3 units left and 2 units up from the origin.

一个点用有序数对 (x, y) 表示。第一个数字是从原点出发的水平距离，第二个数字是垂直距离。例如，点 (−3, 2) 表示从原点向左 3 个单位、向上 2 个单位。

When plotting points, always start at the origin, move along the x-axis first, then move parallel to the y-axis. Label the point clearly if a question asks for coordinates.

描点时，始终从原点出发，先沿 x 轴移动，再沿 y 轴方向移动。如果题目要求写出坐标，要清楚地标出该点。

2. What is a Linear Equation? | 什么是线性方程？

A linear equation is an equation whose graph is a straight line. It has no powers higher than 1, such as x² or x³. For example, y = 2x + 3 is linear, but y = x² + 1 is not.

线性方程是图像为一条直线的方程。它不含高于 1 次的幂，例如 x² 或 x³。比如 y = 2x + 3 是线性方程，而 y = x² + 1 不是。

The most useful form for a straight line is y =

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