A line passes through the points (1, 2) and (3, 8). Find its slope.
["# How to Find the Slope of a Line: A Step-by-Step Guide Using the Points (1, 2) and (3, 8)", "Understanding slope is essential in algebra and geometry because it measures how steep a line is and the direction it heads—upward or downward. Whether you're drawing graphs or solving real-world problems, knowing how to calculate slope is a foundational skill. In this article, we’ll explore step-by-step how to find the slope of a line that passes through the points (1, 2) and (3, 8).", "## What Is the Slope?", "The slope of a line describes the rate at which the line rises (or falls) as you move across the coordinate plane. Mathematically, slope ((m)) is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line:", "[\nm = \frac{y_2 - y_1}{x_2 - x_1}\n]", "Here, ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of two distinct points on the line.", "## Step-by-Step: Finding the Slope from (1, 2) and (3, 8)", "### Step 1: Identify the Given Points\nLet’s assign the points as follows:\n- Point 1: ((x_1, y_1) = (1, 2))\n- Point 2: ((x_2, y_2) = (3, 8))", "### Step 2: Plug Values into the Slope Formula\nSubstitute the coordinates into the slope formula:", "[\nm = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 2}{3 - 1}\n]", "### Step 3: Perform the Calculations\nSimplify both the numerator and the denominator:", "[\nm = \frac{6}{2} = 3\n]", "### Step 4: Interpret the Result\nA slope of 3 means that for every 1 unit increase in the x-direction, the y-value increases by 3 units. Since the slope is positive, the line rises from left to right.", "## Conclusion", "Finding the slope is straightforward when you know two points. By applying the slope formula—rise over run—you can easily determine how steep a line is. In this case, a line passing through (1, 2) and (3, 8) has a slope of 3, indicating a strong upward incline. Mastering this concept empowers you to analyze linear relationships, interpret graphs confidently, and apply math to practical situations.", "Whether you're studying algebra, preparing for standardized tests, or tackling real-life data, understanding slope is essential—and now you’ve learned to calculate it with any two points on a line!"]
