Question

Help. Use two points on the line to find the equation of the line in,standard form

Answer 1

3x - 4y = - 12

Explanation:

The equation of a line in standard form is

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

Calculate the equation in slope- intercept form

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

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m =
`(3-0)/(0+4)` =
`(3)/(4)`

The line crosses the y- axis at (0, 3) ⇒ c = 3

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

Multiply through by 4

4y = 3x + 12 or

3x + 12 = 4y ( subtract 12 from both sides )

3x = 4y - 12 ( subtract 4y from both sides )

3x - 4y = - 12 ← in standard form