Perpendicular lines have negative reciprocal slopes.
Let the slope of the linear equation, y = 1/2x — 4 be m1 = 1/2
And the slope of the line perpendicular to y = 1/2x — 4 as m2,
Then it means that the slope of m2 must be -2 (because if you multiply 1/2 with -2, the result will be - 1).
Now that we have our slope for m2, we can find out the equation of the line by using point (4,1) and slope (m) = -2. Plug these values into the slope-intercept form:
y = mx + b
1 = -2(4) + b
1 = -8 + b
Add 8 to both sides to solve for y-intercept, b:
1 + 8 = -8 + 8 + b
9 = b
Since the y-intercept, b = 9, and slope m2 = -2, we can establish the linear equation of the perpendicular line:
y = -2x + 9
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