Question

The table below represents a linear function. Which relationship represents a function with a lesser slope than the function represented above?

Answer 1

D

Step-by-step explanation

the slope of a line is given by

`\begin{gathered} \text{slope}=(\Delta y)/(\Delta x)=(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}`

Step 1

find the slope of the table

Let

P1(0,3)

P2(2,-2)

replace

`\begin{gathered} \text{slope}=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{replace} \\ \text{slope}=(-2-3)/(2-0)=(-5)/(2)=-(5)/(2)=-2.5 \end{gathered}`

Step 2

find the slope of the line A)

let

P1(-1,3)

P2(-2,1)

replace and calculate

`\begin{gathered} \text{slope}=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{replace} \\ slope_A=(1-3)/(-2-(-1))=(-2)/(-1)=2 \end{gathered}`

Step 3

find the slope of function at B)

we have the equation in slope-intercept form

`\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}`

so

`\begin{gathered} B)y=-(1)/(2)x-3 \\ so \\ \text{slope}=\text{ }(-1)/(2) \end{gathered}`

and

`\begin{gathered} C)y=-(5)/(2)x+1 \\ so \\ \text{slope}=\text{ -}(5)/(2) \end{gathered}`

Step 4

finally, the slope of the line graphed at D)

Let

P1(1,-5)

P2(0,1))

replace

`\begin{gathered} \text{slope}=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1) \\ \text{replace} \\ slope_D=(1-(-5))/(0-1)=(1+5)/(-1)=(6)/(-1)=-6 \end{gathered}`

so, we can conclude

`\begin{gathered} \text{slope(table)}=-(5)/(2)=-2.5 \\ \text{slope(A)}=2 \\ \text{slope(B)}=-(1)/(2)=-0.5 \\ \text{slope(C)}=-(5)/(2)=-2.5 \\ \text{slope(D)}=-6 \end{gathered}`

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