Determining the Slope of a Line

A line "going uphill", moving from left to right, has a positive slope. Only one of the lines, $D,$ slopes upwards.

Similarly, a "downhill" line has a negative slope and a horizontal line has a slope, $m,$ of zero. Therefore,

• $D:$ Positive slope.
• $A:$ Negative slope.
• $C:$ $m=0.$

What about the vertical line, $B?$ We can see what result we get when we try to find its slope using the slope formula. $m = \dfrac{y_2-y_1}{x_2-x_1}$ We need two points, $(x_1,y_1)$ and $(x_2,y_2),$ on the line.

We can use $(7.5, 6)$ and $(7.5, \text{-} 4).$ The slope formula returned a division by $0$ which is undefined. Therefore, the vertical line has an undefined slope. We can now summarize the slopes for all graphs.

• $D:$ Positive slope
• $A:$ Negative slope
• $C:$ $m=0$
• $B:$ Undefined slope