Question

What is the standard form equation of the line shown below?

Graph of a line going through negative 3, negative 1 and 3, 2

(a) y + 1 = one half(x + 3)
(b) y = one halfx + five halves
(c) −x + 2y = 1
(d) x − 2y = −1

Answer 1

D

Explanation:

The equation of a line in standard form is

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

Obtain the equation in point- slope form

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (3, 2)

m =
`(2+1)/(3+3)` =
`(3)/(6)` =
`(1)/(2)`

Use either of the 2 points as the point on the line

Using (- 3, - 1), then

y - (- 1) =
`(1)/(2)`(x - (- 3)), that is

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

Multiply all terms on both sides by 2

2y + 2 = x + 3 ( subtract 2y from both sides )

2 = x - 2y + 3 ( subtract 3 from both sides )

- 1 = x - 2y , that is

x - 2y = - 1 ← in standard form → D