Determine an equation of a line in slope-intercept form that goes through a given point and is parallel or perpendicular to a given line

Question

Write an equation that describes the line that passes through the point (-5,4) and is perpendicular to the graph of y= -1/3x - 1/2

Answer 1

The given line has a slope of -1/3 so a line perpendicular would have a slope of 3.

 

Using y = mx + b, you then have 4 = 3(-5) + b.  Solving for b you get 4 = -15 + b, so b = 19.  Your equation will then be y = 3x + 19.

 

m is the slope, so the original equation had a slope of -1/3.

 

Perpendicular lines have slopes which are opposite reciprocals.  When you multiply the two slopes you get an answer of -1.  -1/3 * 3 = -1

 

If you have the point (-5, 4), x = -5 and y = 4.  Using y = mx + b, this gives you 4 = 3*-5 + b.

                                                                                                                      4 = -15 + b

                                add 15 to both sides to solve for b:                                   19 = b