Solutions

1. \(\text{m} = -\frac{7}{2}\) (Written Solution)

   Step 1: Locate two points on the graph that will be used to find the slope. It is best to choose points with x and y values that are integers, if possible. We will choose \((-2, 3)\) and \((0, -4)\).

   Step 2: Draw a vertical line and a horizontal line to represent the ‘step’ between the two points:

   

   Step 3: Find the rise (or change in y value) and the run (or change in x value).

   

   Step 4: Find the slope. The slope is the change in y value (or how much the line went up or down between the two points) divided by the change in x value (or how much the step moves to the right). The slope is negative since it goes down when we follow the line from left to right. The slope is:

   \({\text{m=}}\frac{\text{change in y}}{\text{change in x}}=\frac{-7}{2}\)

   \({\text{m}}=-\frac{7}{2}\)



2. \(\text{m}=1\)


3. \(\text{m}=-2\)


4. \(\text{m} = \frac{1}{3}\)


5. \(\text{m} = -\frac{2}{5}\)


6. \(\text{m} = 0\)


7. The slope of a vertical line is undefined. (Written Solution)

   Step 1: Locate two points on the graph that will be used to find the slope. Since we don’t have a graph of this line we’ll draw a sample line and include two points so that we can find the slope:

   

   Step 2: Draw a vertical line and a horizontal line to represent the ‘step’ between the two points. In this case, we can only draw a vertical line because there is no change in the x values:

   

   Step 3: Find the rise (or change in y-value) and the run (or change in x-value). The rise, or change in y-value, is 2. There is no change in the x-value so the run is 0.

   Step 4: Find the slope. The slope is the change in y-value (or how much the line went up or down between the two points) divided by the change in x-value (or how much the step moved to the right).

   \({\text{m}}=\frac{\text{change in y}}{\text{change in x}}=\frac{2}{0}\)

   So m = undefined because we can’t divide by zero.