Question

1. Molly says the slope of this line is equal to 1/3.

2. Brian says you can not find the slope of the line when there is a dot that is not plotted perfectly on the intersection of the graph.

Explain who is correct or if neither of them are correct.

Answer 1

The point (5,7) is clearly marked on the graph. So it's a good point to use.

We need another point on this line. Feel free to pick any you want. It's best to go with a point where x and y are both whole numbers. I'll go for (11,9)

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Use the slope formula to find the slope through (5,7) and (11,9)

`\text{Given Points: } (\text{x}_1,\text{y}_1) = (5,7) \text{ and }(\text{x}_2,\text{y}_2) = (11,9)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_2 - \text{y}_1}{\text{x}_2 - \text{x}_1}\\\\m = (9-7)/(11-5)\\\\m = (2)/(6)\\\\m = (1)/(3)\\\\`

The slope is 1/3. Molly is correct.

Brian has a slight point in that the (x,y) in the diagram isn't on a grid marker, so that's probably why he thought finding the slope wasn't possible. But imagine moving the (x,y) to (11,9) to help see why the slope is 1/3.

To go from (5,7) to (11,9) we go up 2, then right 6. This is what the 2/6 refers to. Then 2/6 reduces to 1/3.