Find the equation of lines through the origin ,perpendicular to the line 2x+y=8
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
To find the equation of lines through the origin that are perpendicular to the line 2x+y=8, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
Step 1: Find the slope of the given line.
Rewriting the given line in slope-intercept form (y = mx + b), we have:
2x + y = 8
y = -2x + 8
The slope of this line is -2.
Step 2: Find the negative reciprocal of the slope.
The negative reciprocal of -2 is 1/2.
Step 3: Use the slope (1/2) to write the equation of a line through the origin.
Given that the line passes through the origin, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the point (0, 0) and m is the slope (1/2). Plugging in these values, we get:
y - 0 = (1/2)(x - 0)
Simplifying,
y = (1/2)x
Thus, the equation of lines through the origin that are perpendicular to the line 2x+y=8 is y = (1/2)x.