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.
angle measure conversion

degrees	gradients
-90	-100
0	0
90	100
180	200
270	300

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Let degrees be $x$ - values and gradients be $y$ - values. We can choose two points from the table, for example, $(0,0)$ and $(90,100)$.

Step2: Substitute values into formula

Substitute $x_1 = 0,y_1 = 0,x_2=90,y_2 = 100$ into the slope formula: $m=\frac{100 - 0}{90 - 0}=\frac{100}{90}=\frac{10}{9}\approx1.11$.

Answer:

$1.11$