# Equation for Perpendicular Line

Find the equation of the straight line that is perpendicular to the line 3x + 5y = 7 and passes through the point (-1, 4).

Use this information to answer the questions.

The slope of the new line is:

### Comments for Equation for Perpendicular Line

 Sep 29, 2013 Perpendicular Line by: Staff Answer Part I Find the equation of the straight line that is perpendicular to the line 3x + 5y = 7 and passes through the point (-1, 4). 3x + 5y = 7 is the standard form of the equation rewrite equation in slope-intercept form: y = mx + b 3x + 5y = 7 subtract 3x from each side of the equation 3x + 5y - 3x = 7 - 3x 3x - 3x + 5y = 7 - 3x 0 + 5y = 7 - 3x 5y = 7 - 3x ----------------------------------------------------------

 Sep 29, 2013 Perpendicular Line by: Staff ---------------------------------------------------------- Part II divide each side of the equation by 5 5y = - 3x + 7 5y / 5 = (- 3x + 7) / 5 y = (- 3x + 7) / 5 y = (- 3/5)x + 7/5 the slope intercept form of the equation is y = (- 3/5)x + 7/5 ----------------------------------------------------------

 Sep 29, 2013 Perpendicular Line by: Staff ---------------------------------------------------------- Part III The slope of a line perpendicular to this equation is: m = (-1) * (the reciprocal of -3/5) m = (-1) * (-3/5)⁻¹ m = (-1) * (-5/3) m = 5/3 the slope intercept form of the perpendicular line is: y = mx + b y = (5/3)x + b ----------------------------------------------------------

 Sep 29, 2013 Perpendicular Line by: Staff ---------------------------------------------------------- Part IV Since the perpendicular line passes through the point (-1, 4), you can use this point to solve for b. (-1, 4) means that when x = -1, then y = 4 Substitute the values for x and y into the equation for the perpendicular line, and then solve for b. y = (5/3)x + b 4 = (5/3) * (-1) + b 4 = (-5/3) + b ----------------------------------------------------------

 Sep 29, 2013 Perpendicular Line by: Staff ---------------------------------------------------------- Part V add 5/3 to each side of the equation 4 + 5/3 = (-5/3) + b + 5/3 4 + 5/3 = (-5/3) + 5/3 + b 4 + 5/3 = 0 + b 4 + 5/3 = b b = 4 + 5/3 b = (4)*(3/3) + 5/3 b = 12/3 + 5/3 b = 17/3, or 5 2/3 substitute the value of b into the equation for the perpendicular line y = (5/3)x + b b = 17/3 y = (5/3)x + 17/3 ----------------------------------------------------------

 Sep 29, 2013 Perpendicular Line by: Staff ---------------------------------------------------------- Part VI The final equation for the perpendicular line which passes through the point (-1, 4) is: y = (5/3)x + 17/3 m = slope = 5/3 b = slope intercept = 17/3 The standard form of the perpendicular line can be determined as follows: 3 * y = 3 * ((5/3)x + 17/3) 3y = 5x + 17 3y - 5 x = 5x + 17 - 5x - 5 x + 3y = 5x - 5x + 17 - 5 x + 3y = 0 + 17 - 5 x + 3y = 17 standard form of the perpendicular line - 5x + 3y = 17 a graph of both equations is shown below: ----------------------------------------------------------

 Sep 29, 2013 Perpendicular Line by: Staff ---------------------------------------------------------- Part VII Thanks for writing. Staff www.solving-math-problems.com

 Mar 26, 2018 geometry NEW by: Anonymous to find the equation of the line that is per perpendicular y=-7-17