Question

Which expression can be simplified to find the slope of the line of best-fit in the scatterplot below?

On a graph, a trend line goes through points (4, 35) and (16, 134).
StartFraction 134 minus 35 Over 16 minus 4 EndFraction
StartFraction 134 minus 16 Over 35 minus 4 EndFraction
StartFraction 4 minus 16 Over 35 minus 134 EndFraction
StartFraction 4 minus 16 Over 134 minus 35 EndFraction

Answer 1

To find the slope of the line of best fit from two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the following formula for slope \(m\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

In the given points, we have:
- Point 1: \((4, 35)\) → \(x_1 = 4\), \(y_1 = 35\)
- Point 2: \((16, 134)\) → \(x_2 = 16\), \(y_2 = 134\)

Using the slope formula:

\[
m = \frac{134 - 35}{16 - 4}
\]

Now we can evaluate each of the given expressions:

1. **StartFraction 134 minus 35 Over 16 minus 4 EndFraction**: This matches the slope formula.
2. **StartFraction 134 minus 16 Over 35 minus 4 EndFraction**: This does not match.
3. **StartFraction 4 minus 16 Over 35 minus 134 EndFraction**: This is incorrect for finding the slope.
4. **StartFraction 4 minus 16 Over 134 minus 35 EndFraction**: This is also incorrect.

Therefore, the correct expression that can be simplified to find the slope of the line of best fit is:

\[
\frac{134 - 35}{16 - 4}
\]

So the answer is:

**StartFraction 134 minus 35 Over 16 minus 4 EndFraction**.