Final answer:
Using the slope-intercept form and the given point to find the equation of the line. The equation of the line is y = x - 8.
Step-by-step explanation:
To find the equation of a line parallel to -2x+2y=6 that contains the point (3,-5) in slope-intercept form, we need to follow these steps:
Determine the slope of the given line by rearranging the equation to slope-intercept form: y = mx + b.
In this case, the given line can be rewritten as y = x + 3.
Therefore, the slope of the given line is 1.
Since the line we're looking for is parallel to the given line, it will have the same slope.
So the slope of the line we're looking for is also 1.
Now we can use the slope-intercept form of a line, y = mx + b, and the coordinates of the given point (3,-5) to find the equation of the line.
Substituting m=1, x=3, and y=-5, we have -5 = 1(3) + b.
Solving for b, we find b = -8.
Finally, we can write the equation of the line parallel to -2x+2y=6 that contains the point (3,-5) in slope-intercept form:
=> y = x - 8.