Write an equation in point-slope form of the line with the given characteristics. perpendicular to the line y = 2x - 7; passes through (-3,10)

Question

Please show steps of how you got the answer.

Answer 1

The multiplication of the slopes of perpendicular lines has to be equal -1.

The equation of the given line is written in slope intercept form , y= mx +c, where m is the slope and c is the y intercept. so for y= 2x - 7 , m₁ = 2

let us assume m₂ is the slope of perpendicular line

m_1* m₂ = -1

2* m₂ = -1 dividing both sides by 2

m₂₌ -1/2

the point - slope form is y -y₁ = m ( x - x ₁) where m is the slope of the line and x_1,y₁ any point in the line

y - 10 =( - 1/2) (x + 3)

Answer 2

The perpendicular line MUST have

slope (-1/2)

y + 3 = (-1/2)(x-10)