If a line is perpendicular to another, it means that the slope of the first line is equivalent to the negative reciprocal of the second line. In simple terms, that means the slope of the first line is the same as -1 over the slope of the perpendicular line (-1/m).
So, we just need to do -1/-2 (as -2 is the slope of the perpendicular line) to work out the slope of the first line. -1/-2 is the same as 1/2, or 0.5.
Now, we know the equation of the first line is y = 1/2x + b.
We just need to substitute in the coordinates (6,1) respectively into the x and y values and we get:
(1) = 1/2(6) + b
Now let's simplify:
1 = 3 + b
Now we just need to find the y-intercept (which is b), and to do this, we just need to subtract 3 from both sides of the equation to isolate the b:
1 - 3 = b
-2 = b
Now that we know our b value, we just have to rewrite the whole equation, and you'll have your answer:
y = 1/2x - 2