The equation in point-slope form is:
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
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:
![y=-(5)/(4)x+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/r06r7k1x7ne41n5utdlfwoqhpr3zy0fero.png)
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:
![-9=-(5)/(4)*4+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/ynjstqikaq90ipef6nb30n23iu9ximb7vk.png)
Simplifying:
![-9+5=b](https://img.qammunity.org/2023/formulas/mathematics/high-school/mx7n5ou2jcxb6vc41yh7a1qqy4gjvlvqfu.png)
![b=-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/hxwxnexek4tnqcharhber6ix9exhqiiznn.png)
Answer:
![y=-(5)/(4)x-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/7joxnvor1iu1xh4vid19fqyxu83c809suz.png)