Find the equation of the line passing theough the points (8,-16) and (1,5)

Use y = mx + b (slope intercept form) to calculate the equation of the line, where m represents the slop and b represents the y intercept. 

Slope is equal to the change in y over the change in x, or rise over run. 
m = change in y / change in x

The change in x is equal to the difference in the x coordinates, and the change in y is equal to the difference in y coordinates. 
m= y2 - y1 / x2 - x1

Substitute the values of x and y into the equation to find the slope. 

m = 5 - (-16) / 1 - 8
m = -3

Use slope intercept form to find b. 

Substitute the value of m into the equation. 
y = -3x + b

Substitute the value of x into the equation.
y = (-3)(8) + b
Substitute the value of y into the equation. 
-16 = (-3)(8) + b

Then solve. 
b = 8

Now that the values of m (slope) and b (y-intercept) are known, substitute them into y = mx + b to find the equation of the line. 

y = -3x + 8

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !