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prhsmms

Answer:

[tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

In order to find slope, we need to put this equation into slope-intercept form as shown below.

  • [tex]y=mx+b[/tex]
  • In this case [tex]m[/tex] is slope, and [tex]b[/tex] is the line's y-intercept.

In order to get our equation into this form, we need to isolate [tex]y[/tex] on the left side of the equation. Here's how we do it...

[tex]-x-3y=-6[/tex]

  • First, let's add [tex]x[/tex] to both sides of this equation to get rid of the [tex]-x[/tex] on the left side.

[tex]-3y=-6+x[/tex]    ⇒    [tex]-3y=x-6[/tex]

  • Now, let's divide both sides by [tex]-3[/tex]. This will isolate [tex]y[/tex] on the left side and get our equation into slope-intercept form.

[tex]y=\frac{x}{-3}+\frac{6}{3}[/tex]

  • All we need to do now is simplify. I'll show how I simplified [tex]\frac{x}{3}[/tex] with more than 1 step to make things less confusing hopefully.

[tex]y=\frac{1x}{-3}+2[/tex]

[tex]y=\frac{1}{-3}(\frac{x}{1})+2[/tex]

[tex]y=-\frac{1}{3}x+2[/tex]

  • Our final, simplified answer is shown above.

Now that our formula is in the same format as [tex]y=mx+b[/tex] we know that:

  1. [tex]m=-\frac{1}{3}[/tex]
  2. [tex]b=2[/tex]

Our formula has a slope of [tex]-\frac{1}{3}[/tex] and a y-intercept of [tex]2[/tex].

The slope of this line is -1/3

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