The equation of the line that is parallel to 2x - 2y = 6 and passes through the point (-2,4) is y = x + 6.
To find the equation of a line that is parallel to the line 2x - 2y = 6 and passes through the point (-2,4), we can use the fact that parallel lines have the same slope.
First, let's rearrange the given equation 2x - 2y = 6 into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Starting with 2x - 2y = 6:
-2y = -2x + 6 (subtract 2x from both sides)
y = x - 3 (divide everything by -2)
The slope of this line is 1 because the coefficient of x is 1. So, any line parallel to this line will also have a slope of 1.
Now, we have the slope (m = 1) and a point that the line passes through (-2,4). We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values:
y - 4 = 1(x - (-2))
y - 4 = x + 2
y = x + 6.
Hence, the equation is y=x+6.