The comparison of the given function and the graph is required.
It is true that y-intercept of both functions is 0.
It is false that the slope of both functions is [tex]\dfrac{3}{2}[/tex]
It is true that the graphs function has a greater rate of change.
It is true that point (0,0) is the point of intersection for both the functions.
Function and graphs
Two points of the graph are (0,0),(-2,-3).
The equation of the line is
[tex]y-0=\dfrac{-3}{-2}(x-0)\\\Rightarrow y=\dfrac{3}{2}x[/tex]
The other equation is [tex]y=\dfrac{2}{3}x[/tex]
Both the lines pass through the origin so the y intercept of both the functions is 0.
Only the slope of the function in the graph is [tex]\dfrac{3}{2}[/tex] the other function has slope [tex]\dfrac{2}{3}[/tex]
Writing the decimal forms of the slopes [tex]\dfrac{3}{2}=1.5[/tex] and [tex]\dfrac{2}{3}=0.67[/tex]
The function in the graph does have a greater rate of change.
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