write the equation of the line that is parallel ot the line x + Y =-2 and passed through the origin.
m2 = m1 = -A/B = -1/1 = -1
P(0,0), m2 = -1
Y = mx + b = 0
-1*0 + b = 0
b = 0
Y = -1x + 0
Eq2: Y = -x
To find the equation of a line parallel to a given line and passing through a specific point, the slope of the given line needs to be determined first.
The equation x + y = -2 is in standard form, A*x + B*y = C, where A = 1, B = 1, and C = -2. To determine the slope of this line, rearrange the equation to solve for y:
y = -x - 2
The equation is now in slope-intercept form, y = mx + b, where m represents the slope. In this case, the slope is -1.
Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also -1.
Now, we know the slope of the line, and we also know that it passes through the origin (0,0). We can use the point-slope form of a linear equation to find the equation of the new line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 0 = -1(x - 0)
Simplifying, we get:
y = -x
Therefore, the equation of the line that is parallel to x + y = -2 and passes through the origin is y = -x.