This is a shiny app intended to demonstrate how the value of a gradient changes the slope/shape of a linear plot, and it is aimed for educational purposes.

The Maths

As we know the equation for gradient of a linear equation is:

\[\delta = \frac{Y_2 - Y_1}{X_2 - X_1}\]

Which can be interpreted how much Y changes with each change of 1 unit of X

The app will show students when the bigger the gradient the steeper the slop of the line, and conversely the smaller the gradient the shallower the line

The app is created using shinyapp as web application. The student is asked to move a slider which sets the gradient which is then passed to shiny server as input$grad. This then used to calculate data as follows:

    #We'll assume the gradient slider is set to 5
    grad<-5
    x    <- -5:5 
    y    <- x*grad
    
    #Then we plot the graph as follows:
    plot(x,y,col='red', type="l", ylim=c(-25,25), lwd=3, xaxt="n", yaxt="n")
    axis(1, pos=0)
    axis(2, pos=0)
    abline(v=0, h=0)

Please refer for next slide to check result of this plot

Once the code runs as per previous slide the a line will be plot and displayed as follows:

To check the app please the following link:

https://omarnooreddin.shinyapps.io/gradientexplained/

For the code, please refer to the github repo:

https://github.com/omarmn/DataScience_JH_Coursera_Assignments/tree/master/9.DevelopingDataProdcts/FinalCourseWork

Thanks!