Which equation represents a line that passes through (–9, –3) and has a slope of –6?y – 9 = –6(x – 3)y + 9 = –6(x + 3)y – 3 = –6(x – 9)y + 3 = –6(x + 9)

Hello!The answer is:The last equation,[tex]y+3=-6(x+9)[/tex]Why?To find which of the given equations represents a line that passes through the point (-9,-3) and has a slope of -6, we need to find an equation that can be satisfied by evaluating the given point.We can see that the only equation that can be satisfied evaluating the point (-9,-3) is the last equation:[tex]y+3=-6(x+9)[/tex]Evaluating the point, we have:[tex]-3+3=-6*(-9+9)[/tex][tex]0=-6*(0)[/tex][tex]0=0[/tex]We can see that the equation is satisfied!Also, we can see that evaluating the point into the other equations, they will not be satisfied.Let's prove that:Evaluating:First equation:[tex]y-9=-6(x-3)\\-3-9=-6*(-9-3)\\-12=-6*(-12)=72[/tex]The equation is not satisfied.Second equation:[tex]y+9=-6(x+3)\\-3+9=-6*(-9+3)\\6=-6*(-6)=36[/tex]The equation is not satisfied.Third equation:[tex]y-3=-6(x-9)[/tex][tex]-3-3=-6(-9-9)[/tex][tex]-6=-6(-18)=108[/tex]The equation is not satisfied.Hence, the correct option is the last option, the equation that represents a line that passes through (–9, –3) and has a slope of –6 is the last equation:[tex]y+3=-6(x+9)[/tex]Have a nice day!Note: I have attached a picture for better understanding.