If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis. This slope of this line is undefined. If the line has no x-intercept, then it never intersects the x-axis, so it must be parallel to the x-axis. This means it is a horizontal line, such as .

You have just constructed a best fit line through the data! Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your line bisect (cut in half) the area that encloses the data points.

It’s a mathematically defined line that crosses the Y axis (i.e. where X=0) at zero, also. If the y-intercept is 0, then that means the line passes through the point (0,0) which is also the origin. So, if the y-intercept is 0, then that means the line passes through the origin.

Next, the y-intercept is the value of y when x equals zero. For this example, x represents the new born baby’s birth weight in pounds. If x is equal to 0, this means the baby was born with a weight of 0 pounds.

Zero! This relationship always holds: a slope of zero means that the line is horizontal, and a horizontal line means you’ll get a slope of zero. (By the way, all horizontal lines are of the form “y = some number”, and the equation “y = some number” always graphs as a horizontal line.)

Remark: We usually plot the point where x = 0 (called the y-intercept) and the point where y = 0 (called the x-intercept.)

A positive y-intercept means the line crosses the y-axis above the origin, while a negative y-intercept means that the line crosses below the origin. Simply by changing the values of m and b, we can define any straight line.

The symbol X represents the independent variable. The symbol a represents the Y intercept, that is, the value that Y takes when X is zero. The symbol b describes the slope of a line. It denotes the number of units that Y changes when X changes 1 unit.