Question

Find the equation of the line with an x-intercept of 4 and a y-intercept of -2.

Answer 1

x - 2y = 4

Explanation:

The equation of a line in standard form is

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

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0 ) ← coordinates of intercepts

m =
`(0+2)/(4-0)` =
`(2)/(4)` =
`(1)/(2)`,

Note the y- intercept c = - 2, thus

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

Multiply through by 2

2y = x - 4 ( subtract 2y from both sides )

0 = x - 2y - 4 ( add 4 to both sides )

4 = x - 2y, that is

x - 2y = 4 ← in standard form