How do you write the standard form of a line given (1, 3) and (4, 4)?

1 Answer
SCooke
Apr 8, 2017

#-x + 3y = 8#

Explanation:

First, let’s clarify the line definitions.

Slope Intercept Form: y = mx + b

Point Slope Form: # y – y_1 = m*(x – x_1)#

Standard Form: Ax + By = C ; A must be positive, A, B & C are integers, the coefficient of x is NOT equal to the slope! -A/B = slope; C/B = y-intercept; C/A = x-intercept

First find the slope from the given points. #m = (y_2 – y_1)/(x_2 – x_1)#
#m = (4-3)/(4-1) = 1/3 #
From this we can set A = -1 and B = 3. -x + 3y = C To find C we will need to solve the slope-intercept form for b.

#y = mx + b ; 3 = (1/3)(1) + b ; b = (8/3)# ; #y = (1/3)x + (8/3)#

This can now be rearranged into the desired “Standard Form”:
#-(1/3)x + y = (8/3)# multiply by 3: #-x + 3y = 8#

CHECK:
#-x + 3y = 8# ; #-4 + 3*4 = 8# ; #-4 + 12 = 8# ; #8 = 8# Correct!

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