Question

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 $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Identify points for orange - line

For the orange line with points A(8, 50) and B(12, 90). Using the slope formula: $m_{AB}=\frac{90 - 50}{12 - 8}=\frac{40}{4}=10$.

Step3: Identify points for blue - line

For the blue line with points C(8, 30) and D(12, 60). Using the slope formula: $m_{CD}=\frac{60 - 30}{12 - 8}=\frac{30}{4}=7.5$.

Step4: Compare slopes

Since $10>7.5$, the 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 10, 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.