Question

Write a linear equation in standard form for the line that goes through (2,-5) and (4,-4)

Answer 1

x - 2y = 12

Explanation:

the equation of a line in standard form is

Ax + By = C

where A is a positive integer and B, C are integers

To begin with obtain the equation in slope-intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, - 5 ) and (x₂, y₂ ) = (4, - 4)

m =
`(-4+5)/(4-2)` =
`(1)/(2)`

y =
`(1)/(2)` x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 5), then

- 5 = 1 + c ⇒ c = - 5 - 1 = - 6

y =
`(1)/(2)` x - 6 ← in slope- intercept form

multiply through by 2

2y = x - 12 (add 12 to both sides )

2y + 12 = x ( subtract 2y from both sides )

x - 2y = 12 ← in standard form

Answer 2

Answer: The answer is x-2y=12. Hope I helped