Slope
To describe a line, it is important to indicate how steep it is. This property of the line is called slope. Slope can be any number, including zero (when the line is horizontal). Vertical lines have an infinitely large slope. This lecture series explains how to find the slope of a line given two points and how to graph a line given its slope. Watch the videos and complete the interactive exercises.
Slope in a table - Questions
Answers
1. The slope is \(-1\).
\(\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}\)
We can calculate the change in \(x\) and change in \(y\) by picking any two pairs of corresponding \(x\)- and \(y\)-values.
| \(x\) | 5 | \(\stackrel{+1}{\longrightarrow}\) 6 | \(\stackrel{+1}{\longrightarrow}\) 7 | \(\stackrel{+1}{\longrightarrow}\) 8 |
| \(y\) | -5 | -6 \( \stackrel{-1}{\longrightarrow}\\) | -7\( \stackrel{-1}{\longrightarrow}\\) | -8\( \stackrel{-1}{\longrightarrow}\) |
So the slope is:
\(\frac{\text { Change in } y}{\text { Change in } x}=\frac{-1}{1}=-1\)
The slope is \(-1\).
2. The slope is \(7\).
\(\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}\)
We can calculate the change in \(x\) and change in \(y\) by picking any two pairs of corresponding \(x\)- and \(y\)-values.
| \(x\) | -7 | \(\stackrel{+3}{\longrightarrow}\) -4 | \(\stackrel{+3}{\longrightarrow}\) -1 | \(\stackrel{+3}{\longrightarrow}\) 2 |
| \(y\) | -7 | 14 \( \stackrel{+21}{\longrightarrow}\\) | 35 \( \stackrel{+21}{\longrightarrow}\\) | 56 \( \stackrel{+21}{\longrightarrow}\) |
So the slope is:
\(\frac{\text { Change in } y}{\text { Change in } x}=\frac{21}{3}=7\)
The slope is \(7\).
3. The slope is \(3\).
\(\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}\)
We can calculate the change in \(x\) and change in \(y\) by picking any two pairs of corresponding \(x\)- and \(y\)-values.
| \(x\) | -4 | \(\stackrel{+1}{\longrightarrow}\) -3 | \(\stackrel{+1}{\longrightarrow}\) -2 | \(\stackrel{+1}{\longrightarrow}\) -1 |
| \(y\) | 2 | 5 \( \stackrel{+3}{\longrightarrow}\\) | 8 \( \stackrel{+3}{\longrightarrow}\\) | 11 \( \stackrel{+3}{\longrightarrow}\) |
So the slope is:
\(\frac{\text { Change in } y}{\text { Change in } x}=\frac{3}{1}=3\)
The slope is \(3\).
4. The slope is \( -\frac {2}{5}\)
\(\text { Slope }=\frac{\text { Rise }}{\text { Run }}=\frac{\text { Change in } y}{\text { Change in } x}\)
We can calculate the change in \(x\) and change in \(y\) by picking any two pairs of corresponding \(x\)- and \(y\)-values.
| \(x\) | 31 | \(\stackrel{+5}{\longrightarrow}\) 36 | \(\stackrel{+5}{\longrightarrow}\) 41 | \(\stackrel{+5}{\longrightarrow}\) 46 |
| \(y\) | 10 | 8 \( \stackrel{-2}{\longrightarrow}\\) | 6 \( \stackrel{-2}{\longrightarrow}\\) | 4 \( \stackrel{-2}{\longrightarrow}\) |
So the slope is:
\(\frac{\text { Change in } y}{\text { Change in } x}=\frac{-2}{5}=-\frac{2}{5}\)
The slope is \( -\frac {2}{5}\).