How do you write an equation in standard form for a line passing through (2, -3), m= -3.6?

1 Answer
Jarob R G.
Apr 8, 2018

#18x + 5y = 21#

Explanation:

The standard form of a linear equation is #Ax + By = C#.

Since we are given a slope and a point, the slope-intercept form of a linear equation will quickly provide us with an answer.

Recall that any (non-vertical) line can be written in the form #y = mx + b#, where #m# is our slope and #b# is our initial value. We find #b# by plugging in the provided point and slope:

#y = mx + b#
#y = -3.6x + b#
#-3 = -3.6(2) + b#
#-3 = -7.2 + b#
#4.2 = b#

Thus, our linear equation in slope-intercept form is #y = -3.6x + 4.2#. By moving our term containing #x# to the left-hand side of the equation, we obtain our equation in standard form:

#y = -3.6x + 4.2#
#3.6x + y = 4.2#

We can clean up our answer by multiplying through by #10# to remove our decimals, then simplifying.

#3.6x + y = 4.2#
#36x + 10y = 42#
#18x + 5y = 21#

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