getting equations from coordinates

Question

what is the equation you get from the coordinates (0,-2) (2,0) (4,2)

Answer 1

The equation of a line is in the form y=mx+b, where m is slope and b is y-intercept.

 

The y-intercept is the point on the y axis.  This means that the x value at this point is 0.  The only coordinate point listed here with an x value of 0 is (0, -2).  The y value is -2. 

 

Therefore,  b = -2

 

Next we find the slope.  Slope is rise over run, where the rise is distance in y and the run is distance in x between two points.

 

Let's find the slope using the first two points: (0,-2) and (2,0). 

 

m = (y₂ - y₁) / (x₂ - x₁)

m = (0 - (-2)) / (2 - 0)

m = 2 / 2

m = 1

 

 

Lets find the slope of the last two points: (2,0) and (4,2).

 

m = (2 - 0) / (4 - 2)

m = 2 / 2

m = 1

 

Notice that the two slopes are the same.  This tells us that the coordinates when connected form a straight line.

 

Overall, the slope of the line is 1.

 

 

Your equation is

 

y = x - 2