Question

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

Answer 1

`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`