What is the equation of the line passing through the point (2,3) and perpendicular to the line y = 2x+7

Question

asked Jan 3, 2023 2.2k views

1 Answer

J Castillo · Answer 1 · 2023-01-08T18:28:27+0000

Answer:

y =(-1)/(2)x +4

Explanation:

Equation of the line: y = mx +b

y = 2x + 7

m = 2

Slope of the perpendicular line =
-(1)/(m)

$\sf m_1 =(-1)/(2)$

Equation of the perpendicular line:

y= (-1)/(2)x + b

This line is passing throught (2 ,3). Substitute the x & y coordinate in the above equation and now we can obtain the value of b (y-intercept)

$\sf 3 = (-1)/(2)*2+b\\\\3 = -1 + b\\$

3 + 1 = b

4 = b

Equation:

y =(-1)/(2)x +4