what is the slope of the line thats passes through (4,8) and (-2,1)? what si the equation for this line?

Question

i have been trying for so long and couldnt find the answer

Answer 1

slope = m ="rise over run" the change in y coordinates divided by the corresponding change in x coordinates: (8-1)/(4--2) = 7/6

y=mx + b

y =7x/6 + b

plug in either point to solve for b which = y intercept

8 = 7(4)/6 + b

b = 8-14/3 = 24/3 -14/3 = 10/3

b = 10/3 = y intercept

y=(7/6)x + 10/3

check the answer by plugging in the other point

(-2,1)

1 =(7/6)(-2) + 10/3 =-14/6+20/6 = 6/6 = 1