In order to determine who is correct about the equation of the blue line, you first calculate the slope of the line, by using the following formula:
m = (y2 - y1)/(x2 - x1)
where (x1 , y1) and (x2 , y2) are the coordinates of two point of the line. You can use the points (0 , 8) and (4 , 0). By replacing the coordinates of these points in the formula for the slope m, you obtain:
m = (0 - 8)/(4 - 0) = -8/4 = -2
Next, you use the same formula for the slope but in the following way:
m = (y - y1)/(x - x1)
where (x1 , y1) are the coordinates of some point in the line. You can consider the point (4 , 0):
m = (y - 0)/(x - 4)
you rewrite this expression to obtain the form of the equation of a line
m = (y - 0)/(x - 4) multiply by (x - 4) both sides
m(x - 4) = y
mx - 4m = y replace the obtained value of m
-2x - 4(-2) = y
-2x + 8 = y
y = 8 - 2x
Hence, Roman is correct