I know the answer is 2x+y=8 but I don't know how to get it. Please give me a thorough explanation and some other problems similiar to this question.
Answers:
To get this line, you must first figure out the slope. When a line is parallel to another line, their slopes are the same; however, when they are perpendicular, their slopes are negative reciprocals (flipped fractions) of each other. For example, a line perpendicular to a line with a slope of -3/2 would have a slope of +2/3, and a line perpendicular to a line with a slope of 4 would have a slope of -1/4. The slope of the given equaiton can be found this way:
x-2y=4
x=2y+4
2y=x-4
y=1/2x-2
Since y=mx+b with m being slope and b being y-intercept, then 1/2 is the slope of the given line. Therefore, the slope of the perpendicular line must be the negative reciprocal, which is -2. So far, you have the slope--now you just need the y-intercept. This can be found by substituting the point on the line that you know--the x-intercept--into the equation. An x-intercept of 4 would be found at (4,0) and by plugging this into y=mx+b we can figure out the y-intercept:
y=mx+b
(0)=(-2)(4)+b
0=-8+b
b=8
According to this, the y-intercept is 8. By putting this into the y=mx+b equation, we get the equation:
y=-2x+8
Now, to convert it to the form ax+by=c, we just have to do a bit more math:
y=-2x+8
2x+y=8
And voila, there is your answer. I hope it's not too confusing.
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