Analytical Geometry

Question

Determine which of the following lines is the steepest and why.

 

A)x+2y+8=0

 

B)y=3x+5

 

C) 10=8x+2y

Answer 1

Amber,

 

Steepest refers to the slope. The larger the slope's absolute value, the steeper the line.

 

To find the slope of each line, you can solve the equations for y and read it off from the slop-intercept form y = mx + b.

 

A) y = −(1/2)x − 4  has slope −1/2

 

B) y = 3x + 5 has slope 3

 

C) y = −4x + 5 has slope −4.

 

Since the largest slope numerically is from B), it has the steepest positive slope. But in terms of absolute value, C has the largest steepness, 4. If you teacher makes this distinction, the answer would be C. If positive is counted as steeper than negative, however, the answer is B.