Given:
The line passing through the points ( 0 , -4) and ( 4,1 ) is shown.
We have to find the equation of this line.
The equation of line passing through two points (a,b) and (c,d) is given as:
[tex]y-b=\frac{d-b}{c-a}(x-a)[/tex]
According to the question,
(a , b)= ( 0 , - 4)
(c , d )= ( 4 , 1)
Therefore, the equation of line is given as:
[tex]\begin{gathered} y-(-4)=\frac{1-(-4)}{4-0}(x-0) \\ y+4=\frac{1+4}{4}(x) \\ y+4=\frac{5x}{4} \\ y=\frac{5x}{4}-4 \end{gathered}[/tex]
Therefore, option (C) is correct.
