3. "Which of the following is the equation of the line that is perpendicular to y = 2x - 7 and goes through the points (3,7)?

First, find the slope of the line y = 2x - 7 by comparing with y = mx + b

where m is the slope and b is the intercept

m = 2

Slope of perpendicular lines are inverse of each other

That is;

slope of new equation = - 1/m

= -1 /2

To find the new equation, simply substitute x₁ = 3 y₁ = 7 m = -1/2

into ; y - y₁ = m(x - x₁)

y -7 = -1/2( x - 3)

y - 7 = -1/2 x + 3/2

y = - 1/2 x + 3/2 + 7

y = - 1/2 x + 3+14 /2

y = -1/2 x + 17/2