Question

write the equation of a line perpendicular to 2y+x=4 and passes through the point (2,1) ​

Answer 1

Answer:

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Answer 2

Answer:

$-2x+y=-3$

Step-by-step explanation:

Recall perpendicular lines have negative-reciprocal slopes. Since the equation $2y+x=4$ has a slope of $-\frac{1}{2}$ ($y=-\frac{1}{2}x+2$), any line perpendicular to it will have a slope of $-\frac{1}{-\frac{1}{2}}=2$.

Therefore, we have the line:

$y=2x+b$ where $b$ is the y-intercept.

We can plug in the point it passes through to find the final equation:

$1=2(2)+b,\\b=1-4,\\b=-3$.

Therefore, the equation of the line perpendicular to  $2y+x=4$ that passes through the point $(2, 1)$ is:

$y=2x-3$ (slope-intercept form)

However, since the initial line given is in standard form, re-write this equation to standard form:

$y=2x-3,\\y-2x=-3,\\\fbox{ -2x+y=-3 }$.