Question

Find the slope of each function and determine which has the steeper slope.

Answer 1

Function 1:
x-intercept: (3,0) → a=3
y-intercept: (0,4) → b=4
Slope: m1=?

m=-b/a
m1=-4/3

Function 2:
Point 1: P1=(0,5)=(x1,y1) → x1=0, y1=5
Point 2: P2=(4,8)=(x2,y2) → x2=4, y2=8
Slope: m2=?

m=(y2-y1)/(x2-x1)
m2=(8-5)/(4-0)
m2=3/4

Absolute value (m1)=Absolute value(-4/3)=4/3=1.33
Absolute value (m2)=Absolute value(3/4)=3/4=0.75

Absolute value (m1)=1.33 > 0.75=Abslute value (m2)

Answer: Fourth option: Function 1 has a steeper slope of -4/3 

Answer 2

Function 1 has a slope of 4/3 and Function 2 has a slope of 3/4. This means that Function 1 would be steeper because it goes four units down and 3 units right while Function 2 would be steeper but fall slower because it goes 3 units down and is stretched out more to the right because it goes 4 units to the right making Function 1's line steeper.