Slope
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 \( -\frac {2}{5}\).