To find the slope of the line that represents the conversion of degrees to gradients, we can follow these steps:
1. Identify Two Points:
First, select two points from the given table:
- Point A: [tex]\((-180, -200)\)[/tex]
- Point B: [tex]\((-90, -100)\)[/tex]
2. Calculate the Slope:
The slope ([tex]\( m \)[/tex]) of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting in the coordinates of our selected points:
[tex]\[
m = \frac{-100 - (-200)}{-90 - (-180)} = \frac{-100 + 200}{-90 + 180} = \frac{100}{90} = \frac{10}{9} \approx 1.1111111111111112
\][/tex]
3. Round the Slope:
To provide the slope rounded to the nearest hundredth, we can round 1.1111111111111112.
Rounded to the nearest hundredth, we get:
[tex]\[
1.11
\][/tex]
Therefore, the slope of the line representing the conversion of degrees to gradients is [tex]\( \boxed{1.11} \)[/tex].
