Questions: Angle Measure Conversion Degrees Gradients -180 -200 -90 -100 0 0 90 100 180 200 270 300 Engineers measure angles in gradients, which are smaller than degrees. The table shows the conversion of some angle measures in degrees to angles in gradients. What is the slope of the line representing the conversion of degrees to gradients? Express your answer as a decimal rounded to the nearest hundredth.

Solution Steps

To find the slope of the line representing the conversion of degrees to gradients, we can use the formula for the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] We can use any two points from the table to calculate the slope. For simplicity, let's use the points \((0, 0)\) and \((90, 100)\).

We use the points \((0, 0)\) and \((90, 100)\) from the table to calculate the slope of the line representing the conversion of degrees to gradients.

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \((0, 0)\) and \((90, 100)\): \[ m = \frac{100 - 0}{90 - 0} = \frac{100}{90} = \frac{10}{9} \]

The slope \(\frac{10}{9}\) can be expressed as a decimal: \[ \frac{10}{9} \approx 1.1111 \] Rounding to the nearest hundredth: \[ 1.1111 \approx 1.11 \]

Final Answer