A tangent from a point can be extended in either direction at a time, so how do we determine the direction of electric field at that point?
According to Wikipedia:
A field line is a graphical visual aid for visualizing vector fields. It consists of a directed line which is tangent to the field vector at each point along its length. A diagram showing a representative set of neighboring field lines is a common way of depicting a vector field in scientific and mathematical literature; this is called a field line diagram. They are used to show electric fields, magnetic fields, and gravitational fields among many other types. In fluid mechanics field lines showing the velocity field of a fluid flow are called streamlines.
In usual practice, only finite number of field lines are drawn.
The way to draw obeys some rules. For example, the line density (therefore flux density) is proportional the field strength.
Illustration of Gauss' Law (2D or 3D): For a selected a closed contour (or surface in $3$D), number of outward lines minus the number of inward lines is proportional to the net charge enclosed.
Field line pattern gives a qualitative visualization only. Only direction (with arrows shown or polarities known) of the vector field (but no magnitude) for an arbitray point on a selected field line is known.
For a point not on the field lines drawn, we need to guess the direction (usually more or less parallel to adjacent field lines) when the exact mathematical expression of the vector field is not known.
Alternatively, we can use CAS to plot vector fields on regular lattice points such as Wolfram Alpha:
See also mathematical treatment of electric field pattern in my post here.