How do you write the slope-intercept equation of the line perpendicular to y = 5/2 x - 2, which passes through the point (0, 2)?

1 Answer
May 13, 2017

Answer:

See a solution process below:

Explanation:

The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = color(red)(5/2)x - color(blue)(2)#

Therefore the slope is: #color(red)(5/2)#

Next, let's call the slope perpendicular to this line #m_p#.

The slope of a perpendicular line is: #m_p = -1/m#

Substituting gives:

#m_p = -1/(5/2) = -2/5#

Because the point given in the problem has #0# for the #x# value this is the y-intercept for the perpendicular line. Substituting for #m_p = -2/5# and #2# for #b# into the slope-intercept formula gives:

#y = color(red)(-2/5)x + color(blue)(2)#