Answer:
b = -6 + 10/7 = -32/7
Explanation:
So any line can be defined with a slope and a point. The line is perpendicular to y = 7/5x + 6 which has a slope of 7/5, but we want to find the slope of the line perpendicular. So we take the opposite inverse of 7/5, which is -5/7. So -5/7 is going to be the slope of the line.
Plug this in to the formula for a line:
y = -5/7x + b.
Now we'll solve for b. We were given that it passes through the point (2, -6) meaning that when x = 2, y = -6.
Plug this in and solve for b.
-6 = -5/7 (2) + b
-6 = -10/7 + b
b = -6 + 10/7 = -32/7