As name tells it is an linear line whose equation we find by solving given inputs such as x lables / features and given outputs i.e y labels and through this we calculate paramter such as a,b and we put this in standard equation y = bx + a. It helps us to find output for any desired x values. Below you can see the formula's to calculate a,b constant values.

It's application can be seen in statistics but majorly it used in machine learning,artificial intelligence to predict values.
Like we have three types of learning in AI **1.**Supervised learning**2.**Unsupervised learning**3.**Reinforcement learning

where in we used linear regression in supervised learning where we have multiple feature along with known outputs or we can say an past collected
dataset. So,in this case we trained our model by fitting linear regression line.Then we can simply give any features and this model will calculate
output for us.Many industries are still using this algorithm to simplify their work.