To find the slope of the line representing the conversion of degrees to gradients, we'll use the slope formula. 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:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
From the given table of conversions, we can select any two points to calculate the slope.
Let's choose the points [tex]\((-180, -200)\)[/tex] and [tex]\((-90, -100)\)[/tex].
Assign [tex]\( (x_1, y_1) = (-180, -200) \)[/tex] and [tex]\( (x_2, y_2) = (-90, -100) \)[/tex].
Plug these values into the slope formula:
[tex]\[ m = \frac{-100 - (-200)}{-90 - (-180)} \][/tex]
Simplify the values inside the fraction:
[tex]\[ m = \frac{-100 + 200}{-90 + 180} \][/tex]
[tex]\[ m = \frac{100}{90} \][/tex]
Next, simplify the fraction:
[tex]\[ m = \frac{100}{90} \approx 1.1111 \][/tex]
To express this as a decimal rounded to the nearest hundredth, we get:
[tex]\[ m \approx 1.11 \][/tex]
Therefore, the slope of the line representing the conversion of degrees to gradients is [tex]\( 1.11 \)[/tex].
