Final answer:
To find the equation of the line parallel to y = (1/5)x - 4 and passes through (5,-4), use the point-slope formula and the fact that parallel lines have the same slope. The equation will be y = (1/5)x - 5.
Step-by-step explanation:
To find the equation of the line that is parallel to y = (1/5)x - 4 and passes through the point (5,-4), we need to use the fact that parallel lines have the same slope. The given line has a slope of 1/5, so the parallel line will also have a slope of 1/5.
Using the point-slope formula, we can write the equation as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Plugging in the values, we get y - (-4) = (1/5)(x - 5).
Simplifying, we get y + 4 = (1/5)x - 1. To convert this to slope-intercept form, we subtract 4 from both sides to get y = (1/5)x - 5. Therefore, the equation of the line that passes through the point (5,-4) and is parallel to y = (1/5)x - 4 is y = (1/5)x - 5.