The slope m of a line in the form y=mx+by=mx+b tells us the direction in which the line is pointing. If mm is positive, the line goes into the 1st quadrant as you go from left to right. If mm is large and positive, it has a steep incline, while if mm is small and positive, then the line has a small angle of inclination. If mm is negative, the line goes into the 4th quadrant as you go from left to right. If mm is a large negative number (large in absolute value), then the line points steeply downward. If mm is negative but small in absolute value, then it points only a little downward. If m=0,m=0, then the line is horizontal and its equation is simply y=b.

All of these possibilities are illustrated below.

Interactive Demonstration. Investigate the slope of the line through the point (1,1)(1,1) by moving the red point. Here, green indicates a positive slope, red indicates a negative slope, blue indicates a horizontal line and purple indicates a vertical line.

There is one type of line that cannot be written in the form y=mx+b,y=mx+b, namely, vertical lines. A vertical line has an equation of the form x=a.x=a. Sometimes one says that a vertical line has an “infinite” slope.

It is often useful to find the xx-intercept of a line y=mx+b.y=mx+b. This is the xx-value when y=0.y=0. Setting mx+bmx+b equal to 0 and solving for xx gives: x=−b/m.