Answer:
![b=2](https://tex.z-dn.net/?f=b%3D2)
Step-by-step explanation:
We know that the line passes through the point (16, -10).
And we also know that it is parallel to ![y=-\frac{3}{4}x+8](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B8)
Notice that the slope of this line is -3/4
Remember that parallel lines have the same slope.
Therefore, the slope of our new line is also -3/4
Now, we can use the point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Where <em>m</em> is the slope and (x₁, y₁) is a point.
So, let’s substitute -3/4 for <em>m</em> and (16, -10) for (x₁, y₁). This yields:
![y-(-10)=-\frac{3}{4}(x-16)](https://tex.z-dn.net/?f=y-%28-10%29%3D-%5Cfrac%7B3%7D%7B4%7D%28x-16%29)
Distribute:
![y-(-10)=-\frac{3}{4}x+12](https://tex.z-dn.net/?f=y-%28-10%29%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B12)
Simplify:
![y+10=-\frac{3}{4}x+12](https://tex.z-dn.net/?f=y%2B10%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B12)
Subtract 10 from both sides:
![y=-\frac{3}{4}x+2](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx%2B2)
This is in the form <em>y=mx+b</em>.
Therefore, our <em>b</em> is 2.
And our final answer is 2.