How do you write an equation in standard form for a line passing through (2,9) and (1,3)?

Question

Kennedy Adams · Accepted Answer

Given two points #(x_1,y_1)#  and #(x_2,y_2)#
The slope can be calculated as
#m= (y_1-y_2)/(x_1-x_2)#
For the points given #(2,9)# and #(1,3)#
this gives #m= 6# We can then use this slope plus either one of the given points (I'm going to use #(1,3)# but it shouldn't make any difference)
to write the equation in slope-point form
#y-y_2 = m(x-x_2)#
or for our values
#y-3 = 6(x-1)# Standard form for a line is
#Ax+By=C#
so we shift some values around to get #(-6)x+(1)y = -3#

Jameson Allen · Answer

undefined To write an equation in standard form for a line passing through (2,9) and (1,3), first find the slope using the formula: $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $. Then, use the slope-intercept form $ y = mx + b $ to find the y-intercept $ b $. Once you have the slope and y-intercept, substitute them into the standard form equation $ Ax + By = C $, rearranging if necessary.