Respuesta :

Given

Line is perpendicular to line

[tex]y=\frac{1}{4}x-1[/tex]

and passes through point (4 , 1)

Find

Equation of line in slope intercept form

Explanation

Slope of given line is 1/4

let slope of perpendicular line be m

then

[tex]\begin{gathered} m\times(\frac{1}{4})=-1 \\ m=-4 \end{gathered}[/tex]

then equation of line with slope will be

[tex]y=-4x+b[/tex]

the above line is passing through (4 , 1)

so ,

[tex]\begin{gathered} 1=-4(4)+b \\ 1=-16+b \\ b=17 \end{gathered}[/tex]

so , the required equation of line is

[tex]y=-4x+17[/tex]

Final Answer

Therefore , the required equation of line is y = -4x + 17

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