Question

What is the standard form of the line that has x-intercept 6 and y-intercept -2

Answer 1

x - 3y = 6

Explanation:

The Standard Form of an equation of a line:

`Ax+By=C`

We have the x-intercept and the y-intercept

x-intercept is for y = 0

y-intercept is for x = 0

Therefore we have two points: (6, 0) and (0, -2).

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

Calculate the slope:

`m=(-2-0)/(0-6)=(-2)/(-6)=(1)/(3)`

Put it and the value of y-intercept b = -2 to the equation of a line:

`y=(1)/(3)x-2`

Convert to the standard form:

`y=(1)/(3)x-2` multiply both sides by (-3)

`-3y=-x+6` add x to both sides

`x-3y=6`