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musicluvr31658
The answer is:  "y = -10/3x - 23"

In order to fill in "y=mx+b" you need at least one coordinate and the slope. So first you have to find the slope, using the 2-point slope formula: "m = y2-y1 / x2-x1". It'll look like: "m = -3 - 7 / -6 - -9", after simplifying you get: "m = -10/3". Now that you found slope, you have enough information to fill in the blanks for point slope formula. The point slope formula is: "y - y1 = m (x - x1)". Choose one coordinate, it doesn't matter which one (since the line intersects through both anyways). It'll look like: "y - 7 = -10/3 (x - -9)" OR "y - -3 = -10/3 (x - -6)" (depending on which coordinate you choose). Then you just use basic algebra.
Hello!

First of all if we want to find the equation of the line we will have to find the slope. To do so we will use the equation below.

[tex] \frac{ y_{2} - y_{1} }{ x_{2}- x_{1} } [/tex]

The ones and twos next to the variables just represent that a number came from a certain ordered pair, so for example [tex] x_{1} [/tex] and [tex] y_{1} [/tex] were in their own ordered pair. We can switch the ones and twos and the slope will be the same.

We will have (-9,7) be ([tex] x_{1} ,y_{1}[/tex]), and (-6,-3) be ([tex] x_{2} , y_{2} [/tex]). Now we will plug our numbers into the equation.

[tex] \frac{-3-7}{-6+9} = -\frac{10}{3} [/tex]

The slope of our line is [tex]- \frac{10}{3} [/tex]
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Now we need to solve for the y-intercept. To do so we will substitute a point from our line (-9,7) and solve for b.

7=[tex]- \frac{10}{3} [/tex](-9)+b
7=30+b
b=-23

Therefore, the equation for our line is y=[tex]- \frac{10}{3} [/tex]x-23.

I hope this helps!

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