Final answer:
To find the equation of a line perpendicular to the given line passing through the point (-5,8), we need to determine the slope of the given line, find the negative reciprocal of that slope, and use the point-slope formula to write the equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal of a slope m is -1/m.
The given line is y + 8 = -2/23(x - 5). We can rearrange this equation to slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
After rearranging the equation, we have y = -2/23x + 18/23. The slope of this line is -2/23.
The negative reciprocal of -2/23 is 23/2. So, the slope of the line perpendicular to the given line is 23/2.
Now that we have the slope and a point (-5,8) that the line passes through, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values, we have y - 8 = 23/2(x + 5). Simplifying this equation gives y = 23/2x + 119/2.