Final answer:
To write the equation of a line parallel to y=-2x+1 passing through (-9,-5), use the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. The equation for the line is y + 5 = -2(x + 9).
Step-by-step explanation:
To find the equation of the line that passes through (-9,-5) and is parallel to the line y=-2x+1, we need to determine the slope of the given line and use it to write the equation in point-slope form.
The given line has a slope of -2, that means the parallel line will also have a slope of -2.
Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values (-9,-5) and -2 into the formula to get the equation: y - (-5) = -2(x - (-9)). Simplifying gives us the final equation: y + 5 = -2(x + 9).