How do you find the slope of a line? GRE Math fact

One of the most important properties that define a straight line is its steepness or its incline. Put it simply, a higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

The slope of a line is defined as the ratio of the change in the y coordinates when moving from one point to another to the change in the x coordinates when moving between the same 2 points. Slope is commonly represented using the letter .  If we have two points along the line:  then the slope of the line can be calculated using the formula:

slope formula

Here are some special examples of slopes that you should try to remember:

1. If a line passes through the origin and another point , it’s slope can be represented simply as .
2. A line parallel to the X-axis has a slope of 0 and a line parallel to the Y axis has an undefined slope.

You should also be able to visualize the lines when their slope is provided.

1. A line with a positive slope goes "up" in the positive direction of X-axis i.e. further along you go in the positive direction the higher it goes.

2. A line with a negative slope goes "up" in the negative direction of X-axis i.e. further along you go in the negative direction the higher it goes.

Let’s visualize this so that you understand:

Similarly you should be comfortable in visualizing lines parallel to X and Y axis

Example:

What is the slope of a line that passes through points  and ?

A) 

B) 

C) 

D)  

E)  

Solution:

Here, 

Therefore slope, 

 A is the correct answer.