Answer:
![y=-3x+4](https://img.qammunity.org/2023/formulas/mathematics/high-school/rc4cfmgsj6j0c9fxwk8zphebqq7f43jz4e.png)
For an equation to be perpendicular, the slope must be the negative reciprocal of the other equation.
Given that the slope of the line y = 1/3x + 5 is 1/3,
![(1)/(3)\Rightarrow(-1)((1)/((1)/(3)))=-3](https://img.qammunity.org/2023/formulas/mathematics/college/gnidm4294kk6k4fesl67fpufwshorpst9v.png)
Now we have a slope of -3, we will use the following equation to find the y-intercept of the equation:
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
Using the point (8, -20)
![y=mx+b\Rightarrow-20=(-3)(8)+b](https://img.qammunity.org/2023/formulas/mathematics/college/n6q5398qngmouhfuw6jj39hazlkf8cood8.png)
![-20=-24+b\Rightarrow b=-20+24](https://img.qammunity.org/2023/formulas/mathematics/college/f6sj3kx8qqzzp80cv60qfmvpzlmfpm7md8.png)
![b=4](https://img.qammunity.org/2023/formulas/mathematics/high-school/jqbjioup74un7uzvgylyhqztsylsjc0tr4.png)
Now we got the y-intercept 4. Substituting this to the equation
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
And we will get:
![y=-3x+4](https://img.qammunity.org/2023/formulas/mathematics/high-school/rc4cfmgsj6j0c9fxwk8zphebqq7f43jz4e.png)
Therefore, the equation of the line that passes through the point (8, -20) and is perpendicular to the line y = 1/3x + 5 is:
![y=-3x+4](https://img.qammunity.org/2023/formulas/mathematics/high-school/rc4cfmgsj6j0c9fxwk8zphebqq7f43jz4e.png)