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 line
So,
Slope = m = 4
As we know that the product of slopes of two perpendicular lines is -1
So,
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 form
Learn more about equation of line at:
- brainly.com/question/3375830
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