Question

THE TABLE BELOW REPRESENT A LINEAR FUNCTION.WHICH RELATIONSHIP REPRESENT A FUNCTION WITH A GREATER SLOPE THAN THE FUNCTION REPRESENTED ABOVE?

Answer 1

To answer this question we first need to find the slope of the linear relation given in the table. The slope is given by:

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

We can use any two points in the table to find the slope but to make things easier we are going to use the first two points, then the slope is:

`\begin{gathered} m=(-3-4)/(0-(-4)) \\ =(-7)/(4) \end{gathered}`

Now that we have the slope of the first relation we need to find the slopes of the other relations to compare them.

To find the slope of A we can use the points given in the graph and the formula above, then:

`\begin{gathered} m_A=(-3-2)/(1-0) \\ =-(5)/(1) \\ =-5 \end{gathered}`

then:

`m_A=-5`

To find the slope of the line B we have to notice that the line is given in the slope intercept form:

`y=mx+b`

where m is the slope and b is the y-intercept.

Comparing the expression given and the equation above we conclude that:

`m_B=-(3)/(4)`

To find the slope of the line C we use the same approach as line A. Then:

`\begin{gathered} m_C=(-3-4)/(4-0) \\ =-(7)/(4) \end{gathered}`

hence the slope of lince C is:

`m_C=-(7)/(4)`

Finally to find the slope of line D we compare the equation given with the equation of the line in its slope intercept form above. Then:

`m_D=-(5)/(2)`

Once we know all the slopes we can compare each of them with the slope of the linear relationship given in the table.

Since:

`\begin{gathered} m=-(7)/(4)=-1.75 \\ m_A=-5 \\ m_B=-0.75 \\ m_C=-1.75 \\ m_D=-2.5 \end{gathered}`

Therefore, the linear relationship represented in B is the one with a greater slope than the function from the table. Hence the answer is B.