Respuesta :

Hi student, let me help you out! :)

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We are asked to find the equation of the line, using the given information:

[tex]\star~\mathrm{-3}[/tex], which is the slope

[tex]\star~\mathrm{(1,2)}[/tex] which is a point that the line contains

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

  • The slope is the number before x, in the form [tex]\mathtt{y=mx+b}[/tex].

Since "m" is the slope, and we're given what the slope is, we can substitute -3 for m:

[tex]\dag~\mathtt{y=-3x+b}[/tex]

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Now, we need to find the y intercept, "b", of the line.

Here's how it's done:

Remember the point that the line contains, (1,2)?

Well, its y-coordinate is 2; so what we do is substitute 2 for y:

[tex]\dag~\mathtt{2=-3x+b}[/tex]

Also, its x-coordinate is 1, so we substitute 1 for x:

[tex]\dag~\mathtt{2=-3(1)+b}[/tex]

Now, solve for b:

[tex]\dag~\mathtt{2=-3+b}[/tex]

Add 3 to both sides:

[tex]\dag~\mathtt{2+3=b}[/tex]

Thus, we have

[tex]\dag~\mathtt{5=b}[/tex]

Thus, the equation of the line is:

[tex]\bigstar\underline{\boxed{\mathtt{y=-3x+5}}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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