Answer:
The equation of the line passing through the point (-2,2) and parallel to the line 2x+y=1 is y = -2x - 2.
Explanation:
To find the equation of the line passing through the point (-2,2) and parallel to the line 2x+y=1, we first need to determine the slope of the given line.
The slope of the given line can be found by rearranging the equation in slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.
2x+y=1
y = -2x + 1
So the slope of the given line is -2
Since the line we are looking for is parallel to the given line, it must have the same slope of -2.
We can now use the point-slope form of the equation of a line to find the equation of the line passing through (-2,2) with a slope of -2:
y - y1 = m(x - x1)
where (x1,y1) = (-2,2) and m = -2
Plugging in these values, we get:
y - 2 = -2(x - (-2))
Simplifying the right side:
y - 2 = -2(x + 2)
Expanding:
y - 2 = -2x - 4
Adding 2 to both sides:
y = -2x - 2
So the equation of the line passing through the point (-2,2) and parallel to the line 2x+y=1 is y = -2x - 2.