Question

Find the y-intercept and the slope of the line

9x+3y=6

Write your answers in simplest form.

Answer 1

The slope is
`-3`, and the y-intercept is
`2`.

Step-by-step explanation:

Step 1: Recognize the slope-intercept form

The slope-intercept form of an equation is:

`y=mx+b`

Where
`m` represents the slope, and
`b` represents the y-intercept.

Step 2: Arrange the equation into the slope-intercept form

The equation is given as:

`9x+3y=6`
First of all, let's make
`3y` the subject:

`9x+3y=6\\\\\text{Subtract 9x from both sides:}\\9x+3y-9x=6-9x\\\\\text{Simplify:}\\3y=-9x+6`

Now, let's make
`y` the subject:

`3y=-9x+6\\\\\text{Divide by 3 on both sides of the equation:}\\(3y)/(3)=(-9x)/(3)+(6)/(3)\\\\\text{Simplify}:\\y=-3x+2`

Step 3: Identify the slope and y-intercept

The slope-intercept form of the equation is:

`y=-3x+2`

And the slope-intercept form is:

`y=mx+b`

So,
`m=-3` and
`b=2`.

This means that the slope is
`-3`, and the y-intercept is
`2`.