What is an equation of the line that passes through the point (2,-2) and is perpendicular to the line x-5y=20

To find the equation of the line that passes through the point and is perpendicular to the line , we need to follow these steps:1. Find the slope of the given line .2. Find the slope of the line perpendicular to the given line.3. Use the point-slope form of a linear equation to find the equation of the perpendicular line.Step 1: Find the slope of the given line .To find the slope of the given line, we need to rewrite it in slope-intercept form, which is , where is the slope and is the y-intercept.Rearranging the given equation, we get: The slope of the given line is .Step 2: Find the slope of the line perpendicular to the given line.The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.The negative reciprocal of is .Step 3: Use the point-slope form of a linear equation to find the equation of the perpendicular line.The point-slope form of a linear equation is , where is a point on the line and is the slope.Substituting the point and the slope into the point-slope form, we get: Therefore, the equation of the line that passes through the point and is perpendicular to the line is .