OpenStudy (anonymous):

Find the equation for the line that is perpendicular to the line with the equation -2x+3y=-11 passing through the point (1,-1)

4 years ago
OpenStudy (mathstudent55):

Perpendicular lines have slopes that are negative reciprocals. That means that when you multiply the slopes together you get -1. It also means that if you know the slope of one line, just write that slope as a fraction, then flip it and change the sign to get the slope of the perpendicular. In this problem you want the perpendicular to 2x + 3y = -11. Let's find the slope of the given line. To do that, we solve the equation for y. 2x + 3y = -11 Subtract 2x from both sides: 3y = -2x - 11 Divide both sides by 3 y = (-2/3)x + 11/3 Since this equation is now in the slope-intercept form, y = mx + b, we have the slope, m = -2/3 To find the slope of the perpendicular, we flip the slope and change the sign: Flip it: -3/2. Change sign: m = 3/2 The slope of the perpendicular is 3/2 Now we need to find the equation of a line that passes through point (1, -1) and has slope m = 3/2. For that we use the point-slope equation of a line: y - y1 = m(x - x1), where m = slope, and the point is (x1, y1). y - y1 = m(x - x1) y - (-1) = (3/2)(x - 1) y + 1 = (3/2)(x - 1) Multiply both sides by 2 2y + 2 = 3(x - 1) Distribute the 3 on the right side: 2y + 2 = 3x - 3 Subtract 2y from both sides: 2 = 3x - 2y - 3 Add 3 to both sides: 5 = 3x - 2y Switch sides: 3x - 2y = 5

4 years ago