The equation in point-slope form is:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
We are told the slope of this line. Then, we can replace this value in the equation as follows:
[tex]y=-\frac{5}{4}x+b[/tex]As we have one point (x, y) that passes through this line, we can replace it in the x and y values and solve for b as follows:
[tex]-9=-\frac{5}{4}\times4+b[/tex]Simplifying:
[tex]-9+5=b[/tex][tex]b=-4[/tex]Answer:
[tex]y=-\frac{5}{4}x-4[/tex]
