D
Explanation
the slope of a line is given by
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \\ \text{are 2 points from the line} \end{gathered}[/tex]Step 1
find the slope of the table
Let
P1(0,3)
P2(2,-2)
replace
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{replace} \\ \text{slope}=\frac{-2-3}{2-0}=\frac{-5}{2}=-\frac{5}{2}=-2.5 \end{gathered}[/tex]Step 2
find the slope of the line A)
let
P1(-1,3)
P2(-2,1)
replace and calculate
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{replace} \\ slope_A=\frac{1-3}{-2-(-1)}=\frac{-2}{-1}=2 \end{gathered}[/tex]Step 3
find the slope of function at B)
we have the equation in slope-intercept form
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]so
[tex]\begin{gathered} B)y=-\frac{1}{2}x-3 \\ so \\ \text{slope}=\text{ }\frac{-1}{2} \end{gathered}[/tex]and
[tex]\begin{gathered} C)y=-\frac{5}{2}x+1 \\ so \\ \text{slope}=\text{ -}\frac{5}{2} \end{gathered}[/tex]Step 4
finally, the slope of the line graphed at D)
Let
P1(1,-5)
P2(0,1))
replace
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{replace} \\ slope_D=\frac{1-(-5)}{0-1}=\frac{1+5}{-1}=\frac{6}{-1}=-6 \end{gathered}[/tex]so, we can conclude
[tex]\begin{gathered} \text{slope(table)}=-\frac{5}{2}=-2.5 \\ \text{slope(A)}=2 \\ \text{slope(B)}=-\frac{1}{2}=-0.5 \\ \text{slope(C)}=-\frac{5}{2}=-2.5 \\ \text{slope(D)}=-6 \end{gathered}[/tex]so, the function that has a lesser slopes than the one in the graph is
(D) -6
therefore, the answer is
D
I hope this helps you