EQUATION OF STRAIGHT LINES - 10 MARKS ( KCSE MATHS 2025 ) ( скачать в хорошем качестве

EQUATION OF STRAIGHT LINES - 10 MARKS ( KCSE MATHS 2025 ) (

#equations #straightlines Straight lines #parallel #Equation of straight lines #kcsemathematics #vansikmaths 🇰🇪 📐 The Equation of a Straight Line The equation of a straight line is a fundamental relationship between the horizontal coordinate (x) and the vertical coordinate (y) for every single point that lies on the line. The equation allows you to predict where the line will be on a graph. The most common and useful form of this equation is the **Slope-Intercept Form**, which can be described as: *Y equals M times X plus C* *Y* and *X* represent the coordinates of any point on the line. *M* stands for the *gradient* (or slope). This number tells you the steepness and direction of the line. A positive M means the line slopes up from left to right, while a negative M means it slopes down. *C* stands for the **Y-intercept**. This is the specific point where the line crosses or cuts through the vertical Y-axis. The coordinates of this point are always zero for the x-value and C for the y-value. Calculating the Gradient (M) The gradient, M, is calculated by finding the change in the vertical coordinate (the "rise") and dividing it by the change in the horizontal coordinate (the "run") between any two distinct points on the line. --- 🇰🇪 Straight Lines in the KCSE Curriculum The concept of the straight line equation is heavily tested in the Kenyan Certificate of Secondary Education (KCSE) mathematics exams. Questions often require combining multiple geometric principles: 1. Finding the Equation The main task is often to find the full equation (Y equals M X plus C) given certain information. This information might be: *Two points* on the line: You first use the two points to find the gradient (M), then substitute one of the points and the gradient back into a formula called the *Point-Slope Form* to solve for the Y-intercept (C). *The gradient (M) and one point:* You immediately substitute these values into the Point-Slope Form to find C. 2. Parallel and Perpendicular Lines KCSE questions frequently involve the relationship between two lines: *Parallel Lines:* Lines that never meet. They are characterized by having the **exact same gradient (M)**. If the gradient of the first line is M-one, and the second line is parallel, its gradient M-two must also equal M-one. *Perpendicular Lines:* Lines that meet at a ninety-degree angle. Their gradients have a special relationship: if you multiply the two gradients (M-one times M-two), the answer must always be *negative one**. This means one gradient is the **negative reciprocal* of the other. 3. Intercepts and Rearranging Equations You are often asked to find the points where the line crosses the axes: To find the **Y-intercept**, you set the X-value to zero in the equation and solve for Y. To find the *X-intercept* (the point where the line crosses the horizontal X-axis), you set the Y-value to zero in the equation and solve for X. Questions may also ask for the final equation to be given in the **General Form**, which is where all terms are moved to one side of the equation, usually expressed as A X plus B Y plus C equals zero, where A, B, and C are whole numbers. The equation of a straight line forms the basis of coordinate geometry, connecting algebraic equations to geometric graphs.