What equation of the line through point (2, 1) and perpendicular to the line through (-4, 1) and (3, -2)?

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

Step 1: Find the slope of the line passing through the points (-4, 1) and (3, -2). The slope (m1) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m1 = (y2 - y1) / (x2 - x1) So, m1 = (-2 - 1) / (3 - (-4)) = -3 / 7

Step 2: The slope of the line perpendicular to this line is the negative reciprocal of m1. So, the slope (m2) of the line perpendicular to the given line is: m2 = -1 / m1 = 7 / 3

Step 3: Now that we have the slope of the line we want, we can use the point-slope form of the equation of a line to find the equation of the line. The point-slope form is: y - y1 = m(x - x1) Substituting the point (2, 1) and the slope m2 = 7 / 3, we get: y - 1 = 7/3 * (x - 2)

Step 4: Simplify the equation to put it in the slope-intercept form (y = mx + b). y - 1 = 7/3x - 14/3 So, y = 7/3x - 14/3 + 3/3 Finally, the equation of the line is: y = 7/3*x - 11/3