Answer:
y=-2x-3
Step-by-step 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:
[tex]-x+2y=4\\2y=x+4\\\\y=\frac{x+4}{2}\\\\y=\frac{1}{2}x+2[/tex]
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 [tex]\frac{1}{2}=-2[/tex] (negative reciprocal). Now we must use the point slope formula:
[tex]y=m(x-x_1)+y_1[/tex]
Where m is the slope, x1 is -2 and y1 is 1 (because of the ordered pair given). And so:
[tex]y=-2(x-(-2))+1\\\\y=-2(x+2)+1\\\\y=-2x-4+1\\\\y=-2x-3[/tex]
Therefore, the line that is perpendicular to -x+2y=4 is y=-2x-3.
