Question

Slope=-3 goes through (1,2) whats the equation

Answer 1

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:

$\star~\mathrm{-3}$, which is the slope

$\star~\mathrm{(1,2)}$ which is a point that the line contains

$\triangle~\fbox{\bf{KEY:}}$

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

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

$\dag~\mathtt{y=-3x+b}$

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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:

$\dag~\mathtt{2=-3x+b}$

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

$\dag~\mathtt{2=-3(1)+b}$

Now, solve for b:

$\dag~\mathtt{2=-3+b}$

Add 3 to both sides:

$\dag~\mathtt{2+3=b}$

Thus, we have

$\dag~\mathtt{5=b}$

Thus, the equation of the line is:

$\bigstar\underline{\boxed{\mathtt{y=-3x+5}}}$

Hope it helps you out! :D

Ask in comments if any queries arise.

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