Final answer:
To find the equation of the line that is perpendicular to y = -5x + 3 and passes through (5,-2), we determine the slope of the perpendicular line using the negative reciprocal of the given line's slope (-5). Using the point-slope form of a linear equation, we substitute the given point and slope to find the equation. Finally, rearranging to slope-intercept form gives us the result y = 1/5x - 3.
Step-by-step explanation:
To find the equation of the line that is perpendicular to the line y = -5x + 3 and passes through the point (5,-2), we need to determine the slope of the perpendicular line. The slope of the given line is -5. The slope of a perpendicular line is the negative reciprocal of the slope of the given line, so the slope of the perpendicular line is 1/5.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we substitute in the values (5, -2) for (x1, y1) and 1/5 for m. This gives us the equation y - (-2) = 1/5(x - 5), which simplifies to y + 2 = 1/5x - 1.
Finally, rearranging the equation to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we have y = 1/5x - 3.