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what line is perpendicular to the equation y equals negative 1/4 x - 6 and passes through the point -3, 4

Sagot :

Explanation:

A perpendicular line to the given line has its opposite and reciprocal slope.

The given line y = -1/4x - 6 has a slope of -1/4. Therefore the slope of a perpendicular line is 4:

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

To find the y-intercept b we have to use the point. We replace x = -3 and y = 4 into the equation above and solve for b:

[tex]\begin{gathered} 4=4\cdot(-3)+b \\ 4=-12+b \\ b=4+12=16 \end{gathered}[/tex]

Answer:

The equation of the perpendicular line is y = 4x + 16

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