What is the slope intercept form of the line with a slope of #-2/5 # and y-intercept of # -4/7 #?

1 Answer
Geoff K.
Dec 5, 2016

Simple: #y=-2/5x-4/7#.

Explanation:

Slope-intercept form #(y=mx+b)# is called that because those two pieces of information (the slope #m# and the #y#-intercept #b#) are seen directly in the formula.

Since we are given the value for slope as #m=-2/5# and the value for the #y#-intercept as #b=-4/7#, we simply plug these two values into the raw formula and simplify to arrive at

#y="      "m"     "x+"       "b#

#y=(-2/5)x+(-4/7)#

#y=-2/5x-4/7.#

The slope tells you how fast #y# changes relative to #x# (in this case, #-2/5# times as fast), and the #y#-intercept tells you the value of #y# when #x=0.# If you plug #x=0# into the equation, you get

#y=-2/5(0)-4/7#

#color(white)y=-4/7.#

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