What is an equation of the line that has a y-intercept of -2 and is perpendicular to the line $x - 2 y = 5$ $x-2y = 5$ ?

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Answer 1 · 2015-11-19T15:18:05

$2 x + y = - 2$ $2x+y =-2$

Write as $y_{1} = \frac{1}{2} x - \frac{5}{2}$ $y_1= 1/2x -5/2$

If you have standard form of $y = m x + c$ $y=mx+c$ then the gradient of its normal is $- \frac{1}{m}$ $-1/m$

The gradient of a line normal to this is $- 1 \times {(\frac{1}{2})}^{inverted} = - 2$ $-1 times (1/2)^("inverted") =-2$

As it passes through y=02 at x=0 then the equation becomes:

$y_{2} = - 2 x - 2$ $y_2=-2x-2$

In same form as question gives:

$2 x + y = - 2$ $2x+y =-2$

What is an equation of the line that has a y-intercept of -2 and is perpendicular to the line x-2y = 5x−2y=5x-2y = 5?