Given:
The function is
[tex]y=6x-1[/tex]
To find:
The statement that correctly compares the function shown on this graph and the given function.
Solution:
Slope intercept form of a line is
[tex]y=mx+b[/tex] ...(i)
where, m is slope and b is y-intercept.
We have,
[tex]y=6x-1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=6,b=-1[/tex]
Slope of function is 6 and y-intercept is -1.
The graph passes through (0,-6) and (2,4). So, the y-intercept is -6 and slope is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{4-(-6)}{2-0}[/tex]
[tex]m=\dfrac{10}{2}[/tex]
[tex]m=5[/tex]
Since, 5<6 and -6<-6, therefore, the function shown on the graph has smaller rate of change and a lower starting point.
Hence, the correct option is D.
