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Mathematics

Grade9

Easy

Question

The equation of a line that is perpendicular to the line y - 4x = 7 and passes through the point (5, 2) is ______.

$y = \frac{- 1}{4} x + \frac{13}{4}$
$y = \frac{- 1}{4} x - \frac{13}{4}$
$y = \frac{1}{4} x + \frac{13}{4}$
$y = \frac{1}{4} x - \frac{13}{4}$

hint Hint:

In this question equation of a line is given we have to find the equation of the another line that is perpendicular to the given line also passes through the given point. For this we will first find the slope of the given line by equating it with slope intercept form equation, then we can find the slope of the perpendicular line. At last by point slope form we can find the equation of the required line.

The correct answer is: $y equals fraction numerator negative 1 over denominator 4 end fraction x plus 13 over 4$

Equation of the perpendicular line = y-4x=7
$rightwards double arrow$ y=4x+7
by equating the equation with slope intercept form, we get,
slope of the line, m = 4
So, slope of the required line = $fraction numerator negative 1 over denominator m end fraction$ = $fraction numerator negative 1 over denominator 4 end fraction$
Also, the line passes through the point (5,2).
equation of the required line = $y minus y subscript 1 equals m left parenthesis x minus x subscript 1 right parenthesis$
$rightwards double arrow$ y-2= $fraction numerator negative 1 over denominator 4 end fraction$ (x-5)
$rightwards double arrow$ $y minus 2 equals fraction numerator negative 1 over denominator 4 end fraction x plus 5 over 4$
$rightwards double arrow y equals fraction numerator negative 1 over denominator 4 end fraction plus 5 over 4 plus 2 rightwards double arrow y equals fraction numerator negative 1 over denominator 4 end fraction plus 13 over 4$

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