What is the slope intercept form of the line with a slope of #-1 # that passes through # (-5,7) #?

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Answer 1 · 2017-10-02T01:22:28

See a solution process below:

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.

In the problem we are given: #color(red)(m = -1)#

Substituting this into the formula gives:

#y = color(red)(-1)x + color(blue)(b)#

Next, we can substitute the values from the point in the problem for #x# and #y# and solve for #color(blue)(b)#:

#y = color(red)(-1)x + color(blue)(b)# becomes:

#7 = (color(red)(-1) xx -5) + color(blue)(b)#

#-color(red)(5) + 7 = -color(red)(5) + 5 + color(blue)(b)#

#2 = 0 + color(blue)(b)#

#2 = color(blue)(b)#

Substituting this result into the formula gives:

#y = color(red)(-1)x + color(blue)(2)#