Question

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

Answer 1

`-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!