Final answer:
To find the equation of a line parallel to another line, we use the fact that parallel lines have the same slope. Rearrange the given line equation to determine its slope, which is -5. Use the point-slope form of the equation to find the equation of the line passing through the given point.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. The given line equation is 5x+y=6, so we need to determine its slope. Rearrange the equation in slope-intercept form y = mx + b by isolating y and rewrite the equation as y = -5x + 6. The slope of the given line is -5. Since the line we need is parallel, it will also have a slope of -5. Now we can use the point-slope form of the equation y-y1 = m(x-x1) to find the equation of the line passing through the point (-1,0). Substitute the values into the equation and simplify to get the final equation of the line: y = -5x - 5.