ind the equation of the line that is perpendicular to 𝑦=23𝑥+1 and passes through the point (7,5)

Sure, here are the steps to find the equation of the line that is perpendicular to y=23x+1 and passes through the point (7,5):

1. Find the slope of the given line: The slope of the line y=23x+1 is 23.

2. Find the slope of the line perpendicular to the given line: The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of the line perpendicular to y=23x+1 is -1/23.

3. Use the point-slope form of a line to find the equation of the line: The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting m = -1/23 and (x1, y1) = (7,5) into the equation gives y - 5 = -1/23(x - 7).

4. Simplify the equation to get it into slope-intercept form (y = mx + b): Distribute the -1/23 to get y - 5 = -1/23x + 7/23. Then, add