Find an equation of the line that satisfies the given conditions

Question

Through
(−4, 5);
perpendicular to the line
y = -1/2x + 3

Answer 1

Key ideas...

 

Perpendicular lines have slopes that are opposite reciprocals

 

Thus, the slope of a perpendicular line is the opposite reciprocal of -1/2 which is 2. 

 

Since we are given a point and a slope, we use point slope form to make an equation of a perpendicular line. Remember, point slope form is...

 

y - y₁ = m(x - x₁) 

 

x₁= -4   y₁ = 5  m = 2

 

y - 5 = 2 ( x - (-4)) or simplified... y - 5 = 2(x + 4)

 

If it wants the answer in slope-intercept form, we distribute and switch it to y = mx + b 

 

y - 5 = 2x + 8 .... Then add 5 to both sides...

 

y = 2x + 13

 

Thus are answer is either y - 5 = 2(x + 4) or y = 2x +13