To answer this question we first need to find the slope of the linear relation given in the table. The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]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:
[tex]\begin{gathered} m=\frac{-3-4}{0-(-4)} \\ =\frac{-7}{4} \end{gathered}[/tex]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:
[tex]\begin{gathered} m_A=\frac{-3-2}{1-0} \\ =-\frac{5}{1} \\ =-5 \end{gathered}[/tex]then:
[tex]m_A=-5[/tex]To find the slope of the line B we have to notice that the line is given in the slope intercept form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Comparing the expression given and the equation above we conclude that:
[tex]m_B=-\frac{3}{4}[/tex]To find the slope of the line C we use the same approach as line A. Then:
[tex]\begin{gathered} m_C=\frac{-3-4}{4-0} \\ =-\frac{7}{4} \end{gathered}[/tex]hence the slope of lince C is:
[tex]m_C=-\frac{7}{4}[/tex]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:
[tex]m_D=-\frac{5}{2}[/tex]Once we know all the slopes we can compare each of them with the slope of the linear relationship given in the table.
Since:
[tex]\begin{gathered} m=-\frac{7}{4}=-1.75 \\ m_A=-5 \\ m_B=-0.75 \\ m_C=-1.75 \\ m_D=-2.5 \end{gathered}[/tex]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.