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.


`( 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.


`(-3-7)/(-6+9) = -(10)/(3)`

The slope of our line is 
`- (10)/(3)`
-----------------------------------------------------------
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=
`- (10)/(3)`(-9)+b
7=30+b
b=-23

Therefore, the equation for our line is y=
`- (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.