Which Linear function has the steepest slope

Question

A. Y=-2/5X+3

B. Y=4x-2

C. Y=-6x+1

D. Y= 1/2x-5

 

Answer 1

Each equation is given in slope-intercept form, so you know that the four respective slopes are -2/5 (-0.4 in decimal), 4, -6 and 1/2.

 

The steepest slope is that of the line that is closest to being vertical. This could be a line that has positive slope OR negative slope...the steepest one should be determined by examining the ABSOLUTE VALUES of these four slopes.  This means that line C is the steepest.

Answer 2

All of the equations are in Slope-intercept form:   y = mx + b

      where m is the slope and b is the y-intercept

 

Slope is often called "rise over run" because it measures the (increase in y-values)/(increase in x-values).  You might also see words like "incline" or "grade" to describe slope.

 

Think of a ski slope.  If it goes up 1/2 ft for each foot you travel [see (d)], then it is a tough walk and you may want a ski lift.  And if a rollercoaster goes down 6 feet [a person's height] for each 1 foot away that you travel [see (C) and remember that negative slope goes down], you might get ready to scream.  Finally, think of stairs:  Up 1 step for each step size, so slope ≈ 1.  Now, what are some other slopes that you recognize??

 

"Steepest" means absolute value of m.  So, a slope of -1 and a slope of 1 are equally steep (one down and one up).