Graphing Linear Equations by Hand: A Step-by-Step Guide

Welcome to our lesson on finding points using y-intercept and slope!We'll use the equation y equals two-thirds x plus two as our example.Let's follow these steps to plot our line accurately.First, identify the y-intercept. In our equation, b equals 2.Plot the y-intercept at the point zero comma two on the y-axis.Next, we'll use the slope of two-thirds to find our second point.The slope tells us to move up 2 units for every 3 units right.Let's move right 3 units from our y-intercept.Then move up 2 units to find our second point.This gives us our second point at three comma four.Notice how these movements form a triangle. The ratio of vertical to horizontal movement is our slope, two-thirds.This ratio of rise over run will always equal our slope value.Remember to use the grid intersections for precise plotting. Each small square represents one unit.Now that we have our two points, we're ready to draw our line.Now that we have our two points, we'll connect them with a straight line.Using these points as our guide, we'll draw a straight line and extend it across the coordinate plane.Notice how we extend the line beyond our points to show all possible solutions to our equation.To verify our line is correct, let's choose a third point that appears to lie on the line.We'll substitute x equals 1 into our equation to check if we get y equals 3.Since our calculation gives us y equals 3, which matches our point's y-coordinate, we've confirmed our line is correct.When choosing points to verify, look for coordinates with whole numbers to make calculations easier.For example, points like (2,5) are good choices because they're easy to substitute into our equation.With our line verified, we're ready to explore special cases and common mistakes.First, let's look at special cases in linear equations.A horizontal line occurs when the slope is zero. The equation takes the form y equals a constant.A vertical line has an undefined slope and is written as x equals a constant.Now, let's review common mistakes students make when graphing lines.When dealing with negative slopes, pay special attention to the direction. For negative two-thirds, we go down 2 units for every 3 units right.Here are some important tips for maintaining accuracy in your graphs.Let's review the key points about graphing linear equations.Thanks for learning about special cases and common mistakes in graphing linear equations with Spark.E!