A line passes through the points (1, 2) and (4, 8). Find the slope of the line.
["Understanding the Line Passing Through the Points (1, 2) and (4, 8): Finding Its Slope", "When working with linear equations in math, one of the most fundamental concepts is determining the slope of a line—especially when given two points through which the line passes. In this article, we’ll explore how to calculate the slope of the line that passes through the points (1, 2) and (4, 8), a concept key to algebra, geometry, and real-world applications like calculating rates, gradients, and trends.", "---", "### What Is the Slope of a Line?", "The slope of a line is a measure of its steepness and direction. It quantifies how much the y-value (vertical change) increases (or decreases) relative to a movement along the x-axis (horizontal change). The slope is calculated using the formula:", "[\n\ ext{slope} = \frac{y_2 - y_1}{x_2 - x_1}\n]", "where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points on the line.", "---", "### Given Points", "We are given two points:\n- Point 1: ((1, 2))\n- Point 2: ((4, 8))", "Assign coordinates:\n- (x_1 = 1), (y_1 = 2)\n- (x_2 = 4), (y_2 = 8)", "---", "### Calculating the Slope", "Applying the slope formula:", "[\n\ ext{slope} = \frac{8 - 2}{4 - 1} = \frac{6}{3} = 2\n]", "---", "### Interpretation of the Slope", "A slope of 2 means that for every unit increase in the x-direction (rightward movement), the y-value increases by 2 units. This positive slope indicates a steadily rising line from left to right.", "---", "### Why This Matters", "Knowing how to calculate the slope helps in:\n- Graphing lines accurately on a coordinate plane\n- Interpreting real-life data, such as speed (when x is time, y is distance)\n- Modeling linear relationships in physics, economics, and engineering", "---", "### Summary", "- Points: (1, 2) and (4, 8)\n- Slope formula: (\frac{y_2 - y_1}{x_2 - x_1})\n- Slope = ( \frac{6}{3} = 2 )", "Understanding this simple yet powerful concept opens the door to mastering linear functions and solving complex mathematical problems with confidence.", "---", "Keywords: slope calculation, slope formula, finding slope, line through two points, algebra 101, coordinate geometry, linear equations, mathematics tutorial, slope between (1,2) and (4,8)", "---", "Mastering the slope of a line empowers you to interpret and create linear patterns with precision—essential for both academic success and everyday problem solving."]
