How do you find a standard form equation for the line with #(-4,2)# and #(6,8)#?

1 Answer
Serena D.
Mar 24, 2018

The equation is #-3x+5y=22#

Explanation:

Standard form of an equation: ax+by=c (a, b, and c must be integers)

To find the standard form, first I'll find and write the equation in slope-intercept form.
Slope-intercept form of an equation: y=mx+b, where m is the slope of the line and b is the y-intercept

To find the slope through two points, divide the difference of the y-coordinates by the difference of the x-coordinates

#(y_2-y_1)/(x_2-x_1)#

#(8-2)/(6-(-4))#

#6/10#

#3/5 rarr# This is the simplified slope

So far, the equation is #y=3/5x+b#

To find b, let's plug in one of the points

#8=3/5*6+b#

#8=18/5+b#

#8=3 3/5+b#

#b=4 2/5#

The equation is #y=3/5x+4 2/5# (in slope-intercept form)

#y-3/5x=4 2/5#

#-3/5x+y=4 2/5 rarr# We still have to get rid of the denominators

#-3x+5y=22 rarr# Multiply the equation by 5

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