Final answer:
To find an equation for a line perpendicular to y=-5x-2 and passing through the point (-15,-2), use the point-slope formula and the negative reciprocal of the slope of the given line.
Step-by-step explanation:
To find an equation for a line perpendicular to y=-5x-2 and passing through the point (-15,-2), we first need to determine the slope of the given line. The equation is in the form y = mx + b, where m represents the slope. In this case, the slope is -5. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. So, the slope of the perpendicular line would be 1/5.
Now that we have the slope, we can use the point-slope formula to find the equation of the perpendicular line. The formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the values from the given point and the perpendicular slope, we get y + 2 = (1/5)(x + 15).
Simplifying the equation further, we get y = (1/5)x + 13/5.