Question

Passes through (3, 1) and is perpendicular to the line y=2x+1

Answer 1

y = -1/2 x +5/2

Explanation:

y = 2x+1 is in slope intercept form ( y = mx+b) where 2 is the slope

We want a line perpendicular

Perpendicular lines have slopes that multiply to -1

m * 2 = -1

Divide by 2

m = -1/2

The slope of the perpendicular line is -1/2

y = mx+b

y = -1/2x +b

Using the point (3,1)

1 = -1/2 *3 +b

1 = -3/2 +b

Add 3/2 to each side

2/2 +3/2 = b

5/2 = b

y = -1/2 x +5/2

Answer 2

y = -1/2x + 5/2 or y = -0.5x + 2.5

Explanation:

perpendicular lines have reciprocated slopes (opposite signs and values)

y = 2x + 1 → y = (-1/2x) + b

plug in (3,1) to find b

1 = -1/2(3) + b

1 = -1.5 + b

2.5 = b

y = -1/2x + 5/2 or y = -0.5x + 2.5