The correct answer is Option 3:[tex]y=-\frac{1}{4}x+14[/tex]Step-by-step explanation:Given[tex]y=4x-6[/tex]Point = (8,12)Given equation of line is in slope-intercept form. The co-efficient of x will be the slope of the lineSo,Slope = m = 4As we know that the product of slopes of two perpendicular lines is -1So,Let m_2 be the slope of required line[tex]4*m=-1\\m=-\frac{1}{4}[/tex]The general form will be:[tex]y=m_2x+b[/tex]Putting the value of slope[tex]y=-\frac{1}{4}x+b[/tex]To find the value of b, putting (8,12) in the equation[tex]12=-\frac{1}{4}(8)+b\\12=-2+b\\b=12+2\\b=14[/tex]Putting the values of b and m[tex]y=-\frac{1}{4}x+14[/tex]The correct answer is Option 3:[tex]y=-\frac{1}{4}x+14[/tex]Keywords: Equation of line, Slope-intercept formLearn more about equation of line at:brainly.com/question/3375830brainly.com/question/3398261#LearnwithBrainly