Answer: The correct option is D.
Explanation:
From the figure it is noticed that the f(x) is a straight line so it must be in the form of,
[tex]f(x)=ax+b[/tex]
Where, a coefficient of x and b are constants.
From the graph it is noticed that as the value of x increases the value f(x) decreases. It means the function have negative slope and the coefficient of x must be negative.
The function intersect the y-axis at below the origin. It means the value of b must be negative.
The sign of both constant and coefficient are negative. According to this statement the correct option is D.
In function [tex]f(x)=-5x-19[/tex] both constant and coefficient are negative.
Put x=0, we get f(x)=-19, so the y-intercept is (0,-19).
Put f(x)=0, we get [tex]x=-\frac{19}{5}[/tex], so the x-intercept is [tex](-\frac{19}{5},0)[/tex].
Since both x and y intercepts are negative, therefore option D is correct.
