Answer :
From the given: Slope (m) = -6/5 and point (-9, 0), we will use the Slope-Intercept Form in making the equation.
[tex]\text{ y = mx + b}[/tex]The slope-intercept form is given a y=mx+b where m is the slope and b is the y-intercept at point (0,b).
Let's solve for the y-intercept (b) substituting the slope (m) = -6/5 and (x,y) = (-9,0).
Thus, we get,
[tex]\text{ y =mx + b}[/tex][tex]\text{ 0 = (}\frac{-6}{5})(-9)\text{ + b }\rightarrow\text{ b = -(}\frac{-6\text{ x -9}}{5})\text{ = }\frac{-54}{5}[/tex]Let's now make the equation substituting the slope (m) = (-6/5) and y-intercept (b) = (-54/5). We get,
[tex]\text{ y = (}\frac{-6}{5})x\text{ + (}\frac{-54}{5})[/tex][tex]\text{ y = -}\frac{6}{5}x\text{ - }\frac{54}{5}[/tex]