Question

Write an equation of the line, in standard form, that passes through the points (-2,2) and (4,5). Show all work for credit

Answer 1

x - 2y = - 6

Explanation:

the equation of a line in standard form is

Ax + By = C (A is a positive integer and B, C are integers

To begin find 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, 2) and (x₂, y₂ ) = (4, 5)

m =
`(5-2)/(4+2)` =
`(3)/(6)` =
`(1)/(2)`, hence

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

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

using (- 2, 2), then

2 = - 1 + c ⇒ c = 2 + 1 = 3

y =
`(1)/(2)` x + 3 ← in slope- intercept form

multiply through by 2

2y = x + 6 ( subtract 2y from both sides )

0 = x - 2y + 6 (subtract 6 from both sides )

x - 2y = - 6 ← in standard form

Answer 2

m = (5 - 2) / (4 - (-2)) = 0.5

y = 0.5*(x - 4) + 5 = 0.5*x - 2 + 5 = 0.5*x + 3