I have this plot 

I need to make a straight vertical line at a point on x axis that the user enters and show the coordinates of the intersection of that vertical line with my plot.

How can this be done in MATLAB?

for example: the user enters 1020 then a straight vertical line will be drawn at 1020 that meets the plot at some point and the coordinates of that point will be shown somehow. 

Answers: 

One way to do this is to use the GINPUT function to graphically select a point using the mouse. Assuming the data you plotted is stored in a variable data, the following code should do the sort of thing you want. 

set(gca,'XLimMode','manual','YLimMode','manual');  % Fix axes limits
hold on;
[x,y] = ginput(1);  % Select a point with the mouse
x = round(x);       % Round x to nearest integer value
y = data(x);        % Get y data of intersection
plot([x x],get(gca,'YLim'),'k--');  % Plot dashed line
plot(x,y,'r*');     % Mark intersection with red asterisk
disp('Intersection coordinates:');
disp([x y]);        % Display the intersection point

The above assumes that the x-values of the graph are just indices into the array of data you're plotting, which appears to be the case from the graph you show above.