Answer:
[tex]b=2[/tex]
Step-by-step explanation:
We know that the line passes through the point (16, -10).
And we also know that it is parallel to [tex]y=-\frac{3}{4}x+8[/tex]
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:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let’s substitute -3/4 for m and (16, -10) for (x₁, y₁). This yields:
[tex]y-(-10)=-\frac{3}{4}(x-16)[/tex]
Distribute:
[tex]y-(-10)=-\frac{3}{4}x+12[/tex]
Simplify:
[tex]y+10=-\frac{3}{4}x+12[/tex]
Subtract 10 from both sides:
[tex]y=-\frac{3}{4}x+2[/tex]
This is in the form y=mx+b.
Therefore, our b is 2.
And our final answer is 2.
