Question

Four lines pass through the origin of the given graph. One point lying on each of the four lines has been plotted on the graph. Which of the following line segments has the greatest rate of change?

• A. $\overline{OB}$
• B. $\overline{OA}$
• C. $\overline{OC}$
• D. $\overline{OD}$

Answer 1

The correct option is C $\overline{OC}$

Let’s join every point with the origin to form a line segment.


Slope of AO $=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{-3-0}=\frac{4}{-3}=-1.3$

Slope of BO $=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-0}{-4-0}=\frac{-2}{-4}=0.5$

Slope of CO $=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{1-0}=\frac{2}{1}=2$

Slope of DO $=\frac{y_2-y_1}{x_2-x_1}=\frac{0-0}{4-0}=\frac{0}{4}=0$

Slope of CO > slope of BO > slope of DO > slope of AO

Hence, line segment $\overline{OC}$ has the greatest rate of change.