Final answer:
To find the equation of a line perpendicular to y=(1/5)x-5, we need to determine the slope of the original line and then find the negative reciprocal of that slope. The equation of the perpendicular line with a slope of -5 and passing through the point (-5,6) is y = -5x - 19.
Step-by-step explanation:
To find the equation of a line perpendicular to y = (1/5)x - 5, we need to determine the slope of the original line and then find the negative reciprocal of that slope.
The slope of the original line is 1/5. The negative reciprocal of 1/5 is -5.
So, the equation of the perpendicular line has a slope of -5. Using the given point (-5,6), we can use the point-slope form of a linear equation to write the equation of the perpendicular line.
Using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we have:
y - 6 = -5(x - (-5))
y - 6 = -5(x + 5)
y - 6 = -5x - 25
Finally, rearranging the equation to slope-intercept form (y = mx + b), we have:
y = -5x - 19