Question

What function has the greater slope?Function 1 or function 2

Answer 1

The slope is expressed as

`slope=(y_2-y_1)/(x_2-x_1)`

Given the table of values for function 1 below:

we have

`\begin{gathered} x_1=0 \\ y_1=-3.5 \\ x_2=4 \\ y_2=-1.5 \end{gathered}`

This gives

`\begin{gathered} slope=(-1.5-(-3.5))/(4-0)=(-1.5+3.5)/(4)=(2)/(4) \\ \Rightarrow slope=(1)/(2) \\ \end{gathered}`

For the function 2, we have the graph defined by the line q below:

In the above graph, the line passes through the points (0, -4) and (4, 0).

This implies that

`\begin{gathered} x_1=0 \\ y_1=-4 \\ x_2=4 \\ y_2=0 \end{gathered}`

Thus, we have the slope to be evaluated as

`\begin{gathered} slope=(0-(-4))/(4-0)=(4)/(4) \\ \Rightarrow slope=1 \end{gathered}`

Since function 1 has a slope of 1/2, and function 2 has a slope of 1, we can conclude that

function 2 has a greater