use an visual way to explain to a 12 years boy, why linear equation is called linear

视频信息

答案文本 复制

视频字幕 复制

Hi there! Today we're going to discover something really cool about equations. Have you ever wondered why some equations are called 'linear'? Let's start by looking at a simple equation: y equals 2x plus 1. When we draw this equation on a graph, something amazing happens! Amazing! Do you see what happened? The equation y equals 2x plus 1 created a perfectly straight line! It's as straight as a ruler. This is exactly why we call it a 'linear' equation - because 'linear' means 'relating to a line'. Every linear equation will always make a straight line when you graph it. No curves, no bends, just a perfect straight line! Now let's see what happens with a non-linear equation! Here's y equals x squared. Watch what happens when we graph this equation. See the difference? The linear equation y equals 2x plus 1 makes a perfectly straight line, but y equals x squared makes a curved line called a parabola. That's why we don't call it linear - because it doesn't make a line! Let's look at more examples of linear equations! Here we have y equals 3x minus 2, y equals negative x plus 4, y equals 0.5x, and y equals 5. Watch as I draw each one. See? Every single one makes a perfectly straight line! Some lines go up, some go down, some are steep, some are gentle, and some are completely flat - but they're ALL straight lines. That's what makes them all linear equations! Congratulations! Now you know the secret of why linear equations are called 'linear'! It's because they create straight lines when you graph them. The word 'linear' literally comes from the word 'line'. So whenever you see a straight line on a graph, you know it came from a linear equation. And if you see any curves or bends, then it's not linear. You're now officially a linear equation expert! Great job!