How would you find y=mx+b when given (5,8) and (10, 14)?

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Answer 1 · 2015-04-07T20:03:43

In general, the slope of a line joining points #(x_1,y_1)# and #(x_2,y_2)# is
#m = (y_2 - y_1)/(x_2 - x_1)#

For the given values #(x_1,y_1) = (5,8)# and #(x_2,y_2) = (10,14)#
we have
#m = (14- 8)/(10-5) = 6/5#

Using (arbitrarily) #(x_1,y_1) = (5,8)# as a point
and (not arbitrarily) #m=6/5# as the slope

The slope-point formula for the line can be written as
#(y-8) = 6/5(x-5)#

#rarr 5y - 40 = 6x - 30#
#rarr 5y = 6x +10#

We can convert this to slope-intercept form #y=mx+b#
by dividing both sides by #5#

#y = 6/5x + 2#

The slope is #6/5# and the y-intercept is #2#