Calculate The Slope Of A Line Passing Through (0,-9) And (4,-1)

Hey guys! Today, we're diving into a classic math problem that involves finding the slope of a line. This is a fundamental concept in algebra and geometry, and mastering it will definitely help you tackle more complex problems down the road. So, let's break down this problem step by step and make sure we understand exactly how to calculate the slope. Our main focus here is to understand the slope of a line, which is a key concept in coordinate geometry. Understanding how to calculate slope is super important for understanding linear equations and their graphs. So, grab your thinking caps, and let's get started!

Understanding the Problem

The problem states that line W passes through two points on the coordinate grid: (0, -9) and (4, -1). Our mission, should we choose to accept it (and we do!), is to determine the slope of line W. The slope of a line is a numerical value that describes both the direction and the steepness of the line. It tells us how much the line rises or falls for every unit of horizontal change. In simpler terms, it's how much the 'y' value changes for every change in the 'x' value. A positive slope indicates an upward trend from left to right, while a negative slope indicates a downward trend. A slope of zero means the line is horizontal, and an undefined slope means the line is vertical.

Before we jump into the calculations, let's make sure we understand the significance of the given points. The points (0, -9) and (4, -1) are coordinates on the Cartesian plane. The first number in each pair represents the x-coordinate (horizontal position), and the second number represents the y-coordinate (vertical position). So, (0, -9) means the line passes through the point where x is 0 and y is -9, and (4, -1) means the line passes through the point where x is 4 and y is -1. Visualizing these points on a graph can be super helpful, but for now, let's stick to the math. To find the slope of line W, we'll need a handy-dandy formula that relates the coordinates of two points to the slope. Are you ready to learn the magic formula? Let's go!

The Slope Formula: Our Superpower

The slope formula is the key to solving this problem, and it's a formula you'll want to memorize! It's expressed as:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

Where:

• (x₁, y₁) are the coordinates of the first point
• (x₂, y₂) are the coordinates of the second point

This formula essentially calculates the