How do you write the equation in slope intercept form given (2, 2), (-1, 4)?

2 Answers
BRIAN M.
Jul 6, 2016

The slope-intercept form of the equation is #y=-2/3x+10/3#

Explanation:

The slope-intercept form of the equation of the line is #y=mx+b#
where #m=# slope and #b=# the y intercept

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

#x_1=2#
#y_1=2#
#x_2=-1#
#y_2=4#

#m = (4-2)/(-1-2)#

#m = (2)/(-3)#

#m=-2/3#

Now use the point slope formula to solve for the equation of the line.

#(y-y_1)=m(x-x_1)#

For this situation we are given the slope of #3# and a point of #(2,1)#

#m=-2/3#
#x_1=2#
#y_1=2#

#(y-y_1)=m(x-x_1)#

#(y-2)=-2/3(x-2)#

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

#y cancel(-2) cancel(+2)=-2/3x+4/3 + 2#

#y=-2/3x+4/3 +6/3#

#y=-2/3x+10/3#

EZ as pi
Jul 6, 2016

#y = (-2x)/3 +10/3#

Explanation:

If you have two points on a straight line, there is a lovely formula which allows you to get the equation immediately. It is based on the formula for the slope, so you kill two birds with one stone!

#(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)#

#(y-2)/(x-2) = (4-2)/(-1-2) = 2/-3 " this value is the slope"#

#(y-2)/(x-2) = -2/3" cross multiply"#

#3y - 6 = -2x +4#

#3y = -2x +10#

#y = (-2x)/3 +10/3#

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