The tangent line is a straight line with that slope, passing through that exact point on the graph. To find the equation for the tangent, you'll need to know how to take the derivative of the original equation.
A vertical line has an undefined slope. A line with a positive slope slant upwards, whereas a line with a negative slope slant downwards. How to find the slope of a line using the ratio of rise over run between any two points on the line?