Question

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.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table. For example, take \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(90,100)\).

Step2: Substitute values into the slope formula

Substitute \(x_1 = 0,y_1 = 0,x_2=90,y_2 = 100\) into \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We get \(m=\frac{100 - 0}{90 - 0}=\frac{100}{90}\approx1.11\).

Answer:

\(1.11\)