Question

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

Answer 1

Answer:

x - 3y = 6

Step-by-step 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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Calculate the slope:

$m=\dfrac{-2-0}{0-6}=\dfrac{-2}{-6}=\dfrac{1}{3}$

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

$y=\dfrac{1}{3}x-2$

Convert to the standard form:

$y=\dfrac{1}{3}x-2$            multiply both sides by (-3)

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

$x-3y=6$