Final answer:
To find the equation of a line parallel to 2y - 2 = -2(5 - x) that goes through the point (-15, 14), you first determine the slope of the original line to be -1. Then, you apply the point-slope form using the given point and slope to derive the equation y = -x + 13 which is the desired line's equation.
Step-by-step explanation:
The question is asking to find the equation of a line that is parallel to a given line and passes through a specific point. The original line's equation is 2y - 2 = -2(5 - x). To be parallel, the new line needs to have the same slope. We can rewrite the original equation in slope-intercept form (y = mx + b) to find its slope (m). Simplify the original equation to find that the slope is 1. Then use the point-slope form of a line with the given point (-15, 14) and the slope to write the equation of the line parallel to the given line that passes through the point (-15, 14).
Step 1: Simplify the given equation to get the slope:
2y = 2(5 - x) + 2
2y = -2x + 10 + 2
y = -x + 6
The slope (m) is -1.
Step 2: Write the equation of the parallel line using point-slope form:
(y - y1) = m(x - x1)
(y - 14) = -1 (x - (-15))
y - 14 = -1(x + 15)
Step 3: Simplify the equation to get your final answer:
y = -x - 1 + 14
y = -x + 13. This is the equation of the line parallel to the given line, passing through the point (-15, 14).