What would this be in slope intercept form?

Question

Passes through (4, 7) ; perpendicular to the line
y = 2x + 5

Answer 1

The line equation is  y = 2x + 5 .

y = 2x + 5

Slope of the line m₁ = 2 .

We know that the product of slopes of perpendicular lines is equal -1 .

m_1* m₂  = -1 

_2* m₂  = -1 

m₂  = -1/2 .

The given point is (4,7)

So the point - slope form of equation is y – y₁ = m(x – x₁) .

y – 7 = -1/2(x – 4) 

y – 7 = -1/2x + 2 

y = -1/2x + 2 + 7

y = -1/2x + 9

So the line passes through (4,7) and perpendicular  to  y = 2x + 5 is y = -1/2x + 9 .