How do you write a slope-intercept equation for a line perpendicular to y=2x-4 that contains the point (-6, 2)?

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Answer 1 · 2017-08-23T22:37:58

See a solution process below:

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.

For: #y = color(red)(2)x - color(blue)(4)# the slope is:

#color(red)(m = 2)#

We can substitute this into the formula to give:

#y = color(red)(2)x + color(blue)(b)#

Into this we can substitute the values of the points in the problem for #x# and #y# in the formula and solve for #color(blue)(b)# giving:

#2 = (color(red)(2) xx -6) + color(blue)(b)#

#2 = -12 + color(blue)(b)#

#color(red)(12) + 2 = color(red)(12) - 12 + color(blue)(b)#

#14 = 0 + color(blue)(b)#

#14 = color(blue)(b)#

#color(blue)(b) = 14#

We can now substitute the slope and the value for #color(blue)(b)# into the formula to give the solution as:

#y = color(red)(2)x + color(blue)(14)#