Question

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directions: find the slope of the lines graphed below.
1.
2.
3.
4.
5.
6.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{\text{rise}}{\text{run}}\), where "rise" is the vertical change and "run" is the horizontal change between two points on a line.

Step2: Analyze the first line (Problem 1)

For the first line, if we consider two points on the line, the rise is \(4\) (vertical change) and the run is \(2\). So, \(m = \frac{4}{2}=2\).

Step3: Analyze the second line (Problem 2)

For the second line, the rise is \(- 3\) (negative because it is going down) and the run is \(6\). So, \(m=\frac{-3}{6}=-\frac{1}{2}\).

Step4: Analyze the third line (Problem 3)

For the third line, the rise is \(3\) and the run is \(2\). So, \(m=\frac{3}{2}\).

Step5: Analyze the fourth line (Problem 4)

The fourth line is a vertical line. For a vertical line, the run is \(0\). Since \(m=\frac{\text{rise}}{\text{run}}\) and division by \(0\) is undefined, the slope is undefined.

Step6: Analyze the fifth line (Problem 5)

For the fifth line, the rise is \(-4\) and the run is \(1\). So, \(m=\frac{-4}{1}=-4\).

Step7: Analyze the sixth line (Problem 6)

The sixth line is a horizontal line. For a horizontal line, the rise is \(0\). So, \(m = \frac{0}{\text{run}}=0\) (since the run is non - zero).

Answer:

1. \(2\)
2. \(-\frac{1}{2}\)
3. \(\frac{3}{2}\)
4. Undefined
5. \(-4\)
6. \(0\)