Question

Help please Complete the equation of the line through (-9,7) and (-6,-3) y=mx+b format

Answer 1

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.

$\frac{ y_{2} - y_{1} }{ x_{2}- x_{1} }$

The ones and twos next to the variables just represent that a number came from a certain ordered pair, so for example $x_{1}$ and $y_{1}$ 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 ($x_{1} ,y_{1}$), and (-6,-3) be ($x_{2} , y_{2}$). Now we will plug our numbers into the equation.

$\frac{-3-7}{-6+9} = -\frac{10}{3}$

The slope of our line is $- \frac{10}{3}$
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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=$- \frac{10}{3}$(-9)+b
7=30+b
b=-23

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

I hope this helps!

Answer 2

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.