Find an equation for the linear function g(x) which is perpendicular to the line 5x-8y=32 and intersects the line 5x-8y=32 at x=32 g(x)=

To find the equation of the linear function that is perpendicular to the line and intersects it at , we need to follow these steps:1. Find the slope of the given line .2. Determine the slope of the perpendicular line .3. Find the point of intersection at .4. Use the point-slope form to write the equation of .Step 1: Find the slope of the given line .To find the slope, we can rewrite the equation in slope-intercept form , where is the slope. The slope of the given line is .Step 2: Determine the slope of the perpendicular line .The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.The slope of the perpendicular line is .Step 3: Find the point of intersection at .Substitute into the equation of the given line to find the corresponding -coordinate. So, the point of intersection is .Step 4: Use the point-slope form to write the equation of .The point-slope form of a line is given by , where is a point on the line and is the slope.Using the point and the slope , we can write the equation of as: Simplifying this equation, we get: Therefore, the equation for the linear function is: