What is the point-slope equation of the line through the point (−5, 5) that is perpendicular to the line whose equation is 5x = 3y?

Sure, here are the steps to find the point-slope equation of the line:

Step 1: Find the slope of the given line. The equation of the given line is 5x = 3y. We can rewrite this in slope-intercept form (y = mx + b) to find the slope.

5x = 3y becomes y = 5/3x. So, the slope (m1) of the given line is 5/3.

Step 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 (m2) of the line perpendicular to the given line is -1/(5/3) = -3/5.

Step 3: Use the point-slope form 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.

We know that the line passes through the point (-5, 5) and has a slope of -3/5. Substituting these values into the point-slope form gives us:

y - 5 = -3/5(x - (-5))

This simplifies to:

y - 5 = -3/5x - 3

So, the point-slope equation of the line through the point (-5, 5) that is perpendicular to the line whose equation is 5x = 3y is y - 5 = -3/5x - 3.