Find a general form equation for the line through the pair of points?

Question

#(-7,-2)# and #(1,6)#

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Answer 1 · 2018-06-15T16:37:26

#y=x+5#

The general form of a line is #y=kx+m# where #k,m# are real numbers.

To find #k# which is how steep the line is. We'll use the formula #k={y_2-y_1}/{x_2-x_1}#.

#(-7, -2), (1,6)#

Plug these values into the formula. Note how the first number in the parentheses represents the #x# value and the second #y#.

#k={6-(-2)}/{1-(-7)}={6+2}/{1+7}=8/8=1#

Insert #k# into #y#

#y=1*x+m#

Finally, use one of the points to find #m#, by inserting the #(x,y)# pair into #y#. I'll use the second as i think its eaiser.

#6=1*(1)+m=>m=5#

Therefore, #y=x+5#