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Determining the Slope of a Line

Determining the Slope of a Line 1.6 - Solution

arrow_back Return to 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,D, slopes upwards.

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

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

What about the vertical line, B?B? We can see what result we get when we try to find its slope using the slope formula. m=y2y1x2x1 m = \dfrac{y_2-y_1}{x_2-x_1} We need two points, (x1,y1)(x_1,y_1) and (x2,y2),(x_2,y_2), on the line.

We can use (7.5,6)(7.5, 6) and (7.5,-4).(7.5, \text{-} 4).
m=y2y1x2x1m = \dfrac{y_2-y_1}{x_2-x_1}
m=-467.57.5m=\dfrac{{\color{#009600}{\text{-} 4}}-{\color{#0000FF}{6}}}{{\color{#009600}{7.5}}-{\color{#0000FF}{7.5}}}
m=-100m=\dfrac{\text{-} 10}{0}
The slope formula returned a division by 00 which is undefined. Therefore, the vertical line has an undefined slope. We can now summarize the slopes for all graphs.
  • D:D: Positive slope
  • A:A: Negative slope
  • C:C: m=0m=0
  • B:B: Undefined slope