Exploring Straight Lines

Click on the image to try this on Desmos

If you are feeling a little unsure on identifying the equation of a straight line then use this Desmos graph and experiment by changing the gradient, intercept or points marked on the line. The image above shows the line y=2x+1. We can see that the intercept is 1 (where the line crosses the y axis) and the gradient is 2. Looking at the graph we can see that the gradient is positive and you can verify that the gradient is 2 by dividing the difference between the y coordinates (6 in this image) by the difference in the x coordinates (3 in this image). Try moving the points, you will see that this ratio remains constant.

Compare the second image. We can see that the intercept is 1. Looking at the slope, the gradient is positive. The gradient is given by 2÷4 = 0.5. So the equation of the line is y = 0.5x + 1.

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In the third example; looking at the slope of the line we can see it is negative. The gradient is given by 6÷2 which is 3 and the line crosses the y axis at 2 giving the equation of the line as y = ─3x + 2

Since writing this post Desmos have taken the page and created a superior version!

Gradient of a straight line by Desmos

Try this!