Linear Equations Visualized Step-by-Step

To graph y equals 2x plus 1, we'll start by creating a table of values.Let's plug in x-values from negative 2 to positive 2 to find our y-values.Now we'll plot each point on our coordinate plane.The slope of 2 means that for every 1 unit we move right, we go up 2 units.When we connect these points, we create our line y equals 2x plus 1.Notice how our line passes through the y-intercept at the point zero comma one, exactly where we predicted from our equation.This method of plotting points gives us a precise way to graph any linear equation.Let's explore how linear equations help us understand real-world situations, like cell phone plans.Here's a cell phone plan with a twenty dollar monthly base fee and five dollars per gigabyte of data.This creates a linear relationship between data usage and monthly cost. Let's plot some example usage points.Now, let's compare this with a competitor's plan that has a higher base fee but lower per-gigabyte rate.The point where these lines intersect is our break-even point. At five gigabytes, both plans cost the same.For example, if you use three gigabytes of data, the first plan costs thirty-five dollars, while the competitor's plan costs thirty-seven dollars.We can use our equation to predict costs for any amount of data. For example, six gigabytes would cost fifty dollars.