Final answer:
To find the equation of a line parallel to y = -5x + 3 and passing through (-7,-4), we need to determine the slope of the given line. The slope of the given line is -5, so the equation of the parallel line is y + 4 = -5(x + 7).
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to determine the slope of the given line. In this case, the given line has an equation of y = -5x + 3, which means the slope is -5. Since parallel lines have the same slope, the line we are looking for will also have a slope of -5.
Given that the line passes through the point (-7,-4), we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the given point (-7,-4) and the slope -5, the equation of the line is: y - (-4) = -5(x - (-7)). Simplifying, we get: y + 4 = -5(x + 7). This is the equation of the line passing through (-7,-4) and parallel to y = -5x + 3.