Question

What is an equation of the line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ?

Answer 1

y=-2x-3

Explanation:

Since our equation is in standard form Ax+By=C we must first manipulate the equation so that we have it in the slope-intercept form such that y=mx+b. Therefore:

`-x+2y=4\\2y=x+4\\\\y=(x+4)/(2)\\\\y=(1)/(2)x+2`

Therefore, our slope is 1/2 and our y-intercept is 2. Now in order to determine a perpendicular line to the one stated above we must then get the negative inverse of our slope meaning
`(1)/(2)=-2` (negative reciprocal). Now we must use the point slope formula:

`y=m(x-x_1)+y_1`

Where m is the slope, x1 is -2 and y1 is 1 (because of the ordered pair given). And so:

`y=-2(x-(-2))+1\\\\y=-2(x+2)+1\\\\y=-2x-4+1\\\\y=-2x-3`

Therefore, the line that is perpendicular to -x+2y=4 is y=-2x-3.