Good question.

I am assuming you are asking about the graph of a straight line. The easiest way is to consider the following equation of the straight line y = mx + b where m is the slope and b is the y-intercept.

The y-intercept is determined by looking at where the graph intersects with the y-axis (vertical axis). E.g. if the point where the graph crosses (or intersections with) the y-axis is (0, 4) then the y-intercept is 4 .

Second is to find the slope. Pick any two points on the line. Let's say the two points are (x_1, y_1) and (x_2, y_2) . Then the slope of the line is given by \frac{y_2 - y_1}{x_2 - x_1} .

Having found both m and b , we can write the equation of the straight line as y = mx + b .

Let's apply this to the following graph:

The point where the line crosses the y-axis is denoted by A which is (0, 1) . Therefore, the y-intercept is 1 .

The two points that we have selected to calculate the slope are A and B which are (0, 1) and (1.5, 0) . Therefore, the slope is \frac{0 - 1}{1.5 - 0} = -\frac{2}{3} . Therefore, the equation of the straight line is y = -\frac{2}{3} x + 1 .