Answer:
[tex]y =\dfrac{-1}{2}x +4[/tex]
Step-by-step explanation:
Equation of the line: y = mx +b
y = 2x + 7
m = 2
Slope of the perpendicular line = [tex]-\frac{1}{m}[/tex]
[tex]\sf m_1 =\dfrac{-1}{2}[/tex]
Equation of the perpendicular line:
[tex]y= \dfrac{-1}{2}x + b[/tex]
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)
[tex]\sf 3 = \dfrac{-1}{2}*2+b\\\\3 = -1 + b\\[/tex]
3 + 1 = b
4 = b
Equation:
[tex]y =\dfrac{-1}{2}x +4[/tex]
