The slope of the line is negative and its y-intercept is positive; therefore, we need to look for an equation that has this form.
Let us convert all the equations in the slope-intercept form and see which one has the desired properties.
(A). The equation can be rewritten as
[tex]y=\frac{5}{3}x+1[/tex]this has a positive slope and a positive y-intercept - not the correct choice.
(B).
[tex]y=-\frac{5}{3}x-1[/tex]this has a negative slope and a negative y-intercept - also not a correct choice.
(C).
[tex]y=-\frac{5}{3}x+1[/tex]this has a negative slope and a positive y-intercept; therefore, this is the correct choice!
(D).
[tex]y=-\frac{5}{3}x+1[/tex]this equation has a negative slope and a positive y-intercept; therefore, this is also a correct choice.
