Question

Use the equation in standard form 3x + 6y = 8 to determine the slope m and the y-intercept b of the line. Answers: m = and b =

Answer 1

Hello :)

Answer -

Slope: -1/2

Y-intercept: 4/3

Step-by-step explanation -

Our task is to find the slope and the y-intercept of the line whose equation is
`\sf{3x+6y=8}`.

First, I'll write the equation in slope intercept.

`\begin{gathered}\sf{3x+6y=8}\\\sf{6y=8-3x}\\\sf{y=\cfrac{8}{6}-\cfrac{3}{6}x}\\\sf{y=\cfrac{4}{3}-\cfrac{1}{2}x}\\\sf{y=-\cfrac{1}{2}x+\cfrac{4}{3}}\end{gathered}`

Slope: -1/2 (the number in front of x)

Y-intercept: 4/3 (the constant term)

Answer 2

m = -
`(1)/(2)` , b =
`(4)/(3)`

Explanation:

the equation of a line in slope- intercept form is

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

given

3x + 6y = 8 ( subtract 3x from both sides )

6y = - 3x + 8 ( divide through by 6 )

y = -
`(3)/(6)` x +
`(8)/(6)` , that is

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

with slope m = -
`(1)/(2)` and y- intercept b =
`(4)/(3)`