Question

math and graphing tutorial
the slope of the orange line between points a and b is
, and the slope of the blue line between points c and d is
. the mathematical slope of the steeper line is
the slope of the less - steep line.

Explanation:

Step1: Recall slope formula

The slope formula is $m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Assume coordinates for A and B

Let's assume $A=(x_1,y_1)$ and $B=(x_2,y_2)$. Suppose $A=(8,50)$ and $B=(10,90)$. Then for the orange - line between A and B, $m_{AB}=\frac{y_2 - y_1}{x_2 - x_1}=\frac{90 - 50}{10 - 8}=\frac{40}{2}=20$.

Step3: Assume coordinates for C and D

Let's assume $C=(x_3,y_3)$ and $D=(x_4,y_4)$. Suppose $C=(8,30)$ and $D=(12,60)$. Then for the blue - line between C and D, $m_{CD}=\frac{y_4 - y_3}{x_4 - x_3}=\frac{60 - 30}{12 - 8}=\frac{30}{4}=7.5$.

Step4: Compare slopes

Since $20>7.5$, the mathematical slope of the steeper line (orange line) is greater than the slope of the less - steep line (blue line).

Answer:

The slope of the orange line between points A and B is 20, and the slope of the blue line between points C and D is 7.5. The mathematical slope of the steeper line is greater than the slope of the less - steep line.