Answer:
Option: D is the correct answer.
D) [tex]y=\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
A line is said to be steepest if the modulus of the slope is greatest and it is least steep if the modulus of the slope i.e. |m| is least.
We know that the slope intercept form of a line is given by:
[tex]y=mx+c[/tex]
where m is the slope of the line and c is the y-intercept of the line.
A)
[tex]y=4x-3[/tex]
The slope of line is: 4
i.e. m=4
and |m|=4
B)
[tex]y=\dfrac{-3}{4}x+5[/tex]
the modulus of slope is:
[tex]|m|=\dfrac{3}{4}=0.75[/tex]
C)
[tex]y=-10x-8[/tex]
The modulus of slope of line is:
[tex]|m|=10[/tex]
D)
[tex]y=\dfrac{1}{2}x+2[/tex]
The slope of the line is:
[tex]|m|=\dfrac{1}{2}=0.5[/tex]
The modulus of slope of line in options D is smallest.
Hence, the line in option: D is least steep.
