How to write the equation of a line that passes through the points (-1,3) and (1,-1)

y = -2x + 1

Solution:

To find the the equation use first find the slope using the equation:

m= y2-y1/x2-x1

m = -1-3/1-(-1)

m = -4/2

m = -2

Using the equation below,

y = mx + b  

y = y coordinate  

m = slope  

x = x coordinate  

b = y intercept  

so to write the equation of line we need to find the y-intercept (b)  

substitute the slope (-2) and any of the given pair of coordinates ,  right now i will be using (1,-1)

y = mx + b  

-1 = (-2)(1) + b

-1+2 = b

1 = b

So the line of equation,

y = mx + b  

y = -2x + 1

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).