[Math] the meaning of “slope of the line at a point”

Question

I am new to calculus and until now i knew that slope of a straight line is the rate of change of the y-coordinate with respect to the change in x-coordinate of the straight line or the rise over run and to calculate it we need at least two points.
Now, i recently encountered a statement where the phrase "slope of the line at a point" is used. What does this really mean? Don't we need two points to calculate the slope of a line? How come there exists a slope for a point in a line and isn't slope a property of the line and not the point?

Answer 1

See the plot:

First we have to define the slope of a straight line. Then "slope of a curved line at a point" means the slope of the tangent to the curve at that point and this is equivalent to bringing two points on the curve so close to each other that there will be negligible difference between them and then finding the slope of the line passing through the two infinitesimally close points and this line can be regarded as a tangent line.