Question

Question #4ece9

Answer 1

`y= -11/2 x -52`

Explanation:

We know that the general equation of a line is:

`y = mx + c`

Where `m` is your gradient

Now we must find `m`:

`m =`(change in `y`)`/`(change in `x)` = `( Delta y) / (Delta x)`

Change in `y: -8 - (3) = -11`

Change in `x: -8 - (-10) = 2`

`=> m = -11/2`

so hence `y = -11/2 x +c`

Now to find `c`, we must input one of the points into the equation anf then solve for `c`:

Inputing`(-8,-8)`

( we could input either of the points that lie on the line)

`-8 = (-11/2 * -8) +c`

`-8 = 44 + c`

Minusing 44 from both sides:

`-52 = c`

hence our line equation is:

`y= -11/2 x -52`

Hope this helped

Answer 2

The answer to your problem is y= -11/2 x -52

Explanation:

You start by putting the points in the equation that is y = ax +b
In your case, the first point is (-10,3) which means that if x is -10 then y is 3. So you put it in the main formula which results in
3 = a(-10) + b.
Now you have two unknowns but luckily you have two points so you want to see whats the correlation between a and b:
3 = -10 a + b
<=> 3 + 10 a = b.
Then you enter your second point which is (-8,8): 8 = -8 a + b
But because you know what b is you can write it in the "a form" =>
8 = -8 a + 3 + 10 a
<=> -8-3 = -8a +10a
<=> -11 = 2a
<=> -11/2 = a
Now that you know a you can put it in the original line
3 = -10(a) +b
<=> 3 = -10(-11/2) +b
<=> 3 - 55 = b
<=> -52 = b
The last step is to put it in the main equation:
y = -11/2 x -52

Answer 3

`11x+2y=-104`

Explanation:

Note: I modified the question to delete duplication of the point `(-10,8)` (which might have caused some confusion).

Given 2 points, we will assume that the required equation is that of a straight line.
On a straight line the slope (the difference between the `y` coordinate values divided by the difference between the `x` coordinate values) is the same for any pair of points on the line.

Consider the general point `(x,y)` and the given specific points `(-10,3)` and `(-8,-8)`

Slope`= (y-3)/(x-(-10))=(3-(-8))/(-10-(-8))`

Simplifying:
`color(white)("XXX")(y-3)/(x+10)=11/(-2)`

`color(white)("XXX")(-2)(y-3)=11(x+10)`

`color(white)("XXX")6-2y=11x+110`

`color(white)("XXX")-11x-2y=104`

`color(white)("XXX")11x+2y=-104`
(which is the "standard form" for a linear equation)