To find the equation of a line perpendicular to the given line and passing through the origin, we first need to find the slope of the given line.
2x + y = 8
Rearranging the equation to slope-intercept form (y = mx + b) gives:
y = -2x + 8
The slope of this line is -2.
A line perpendicular to this line will have a slope that is the negative reciprocal of -2. The negative reciprocal of -2 is 1/2.
So, the slope of the line we are looking for is 1/2.
Now, we can use the slope-intercept form (y = mx + b) with the known slope of 1/2 and the fact that it passes through the origin (0,0). Plugging in these values gives:
0 = (1/2)(0) + b
0 = 0 + b
b = 0
Therefore, the equation of the line that is perpendicular to 2x + y = 8 and passes through the origin is:
y = (1/2)x
Find the equation of lines through the origin ,perpendicular to the line 2x+y=8
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