Answer:
y = 2x - 4
Step-by-step explanation:
The equations are put in slope intercept form
Slope intercept form: y = mx + b
Where m = slope and b = y intersect
So in order to find the equation of the data represented by the table we will have to find the slope and y intercept
Let's begin!
First let's find the slope
We can find the slope by using the slope formula
m = (y2 - y1) / (x2 - x1) where the x and y values are derived from coordinates from the table
The points chosen may vary but I have chosen the points (0,-4) and (1,-2)
Now that we have chosen the points we will use to find the slope let's define the variables
remember coordinates are written like this: (x,y)
The x value of the second coordinate is 1 so x2 = 1
The x value of the first coordinate is 0
So x1 = 0
The y value of the second coordinate is -2 so y2 = -2
The y value of the first coordinate is -4
So y1 = -4
Now that we have defined each variable let's plug in the values into the formula
Formula: m = (y2 - y1) / (x2 - x1)
Variables: x2 = 1, x1 = 0, y2 = -2, y1 = -4
Substitute values
m = (-2 - (-4) / ( 1 - 0 )
Evaluate
The negative signs cancel out on top and it changes to +4
m = (-2 + 4)/(1-0)
Add top values
m = 2/(1-0)
Subtract bottom numbers
m = 2/1
Simplify fraction
m = 2
So we can conclude that the slope (m) = 2
Now let's find the y intercept or "b"
The y intercept is the value of y when x = 0
If you look at the table when x = 0 y = -4 meaning that the y intercept or "b" is -4
Now that we have found everything let's find the equation of the data represented by the table
The equation is in slope intercept form
y = mx + b
Define variables
m = 2 and b = -4
Substitute values
y = 2x - 4
The equation is y = 2x - 4
, the slope is 
.
, the slope is 
, that's the slope.
, so it would be put together like this:![y=[tex]- \frac{1}{2}x+3=2x-4\\ -\frac{1}{2}=2x-7\\ 1\frac{1}{2}x=-7\\ x=-4.66667](https://tex.z-dn.net/?f=y%3D%5Btex%5D-%20%5Cfrac%7B1%7D%7B2%7Dx%2B3%3D2x-4%5C%5C%20-%5Cfrac%7B1%7D%7B2%7D%3D2x-7%5C%5C%201%5Cfrac%7B1%7D%7B2%7Dx%3D-7%5C%5C%20x%3D-4.66667)