Answer:
The correct option is C.
Step-by-step explanation:
The given function is
[tex]y-4=\frac{4}{3}(x-2)[/tex] ..... (1)
The point slope form of a linear function is
[tex]y-y_1=m(x-x_1)[/tex] ..... (2)
Where, m is slope and the graph passing through the point [tex](x_1,y_1)[/tex].
From (1) and (2), we get
[tex]m=\frac{4}{3},x_1=2,y_1=4[/tex]
It means the slope of the line is positive and the graph passing though the point (2,4).
Put x=0 in the given function, to find the y-intercept.
[tex]y-4=\frac{4}{3}(0-2)[/tex]
[tex]y-4=\frac{-8}{3}[/tex]
[tex]y=\frac{-8}{3}+4[/tex]
[tex]y=\frac{-8+12}{3}[/tex]
[tex]y=1.333[/tex]
The y-intercept is 1.333.
Put y=0 in the given function, to find the x-intercept.
[tex]0-4=\frac{4}{3}(x-2)[/tex]
[tex]-12=4x-8[/tex]
[tex]-4=4x[/tex]
[tex]x=-1[/tex]
The x-intercept is -1.
Therefore option C is correct.
