select all of the points that could be on a line with the point (10,1) if the line has a negative slope.\na…

select all of the points that could be on a line with the point (10,1) if the line has a negative slope.\na (2,6)\nb (-1,0)\nc (-4,7)\nd (11,0)\ne (2,-2)

select all of the points that could be on a line with the point (10,1) if the line has a negative slope.\na (2,6)\nb (-1,0)\nc (-4,7)\nd (11,0)\ne (2,-2)

Answer

Explanation:

Step1: Recall the slope formula

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}), where ((x_1,y_1)=(10,1)) and ((x_2,y_2)) is the other point. We want (m<0).

Step2: Calculate slope for option A

For point ((2,6)): (m=\frac{6 - 1}{2 - 10}=\frac{5}{-8}=-\frac{5}{8}<0)

Step3: Calculate slope for option B

For point ((-1,0)): (m=\frac{0 - 1}{-1 - 10}=\frac{-1}{-11}=\frac{1}{11}>0)

Step4: Calculate slope for option C

For point ((-4,7)): (m=\frac{7 - 1}{-4 - 10}=\frac{6}{-14}=-\frac{3}{7}<0)

Step5: Calculate slope for option D

For point ((11,0)): (m=\frac{0 - 1}{11 - 10}=\frac{-1}{1}=-1<0)

Step6: Calculate slope for option E

For point ((2,-2)): (m=\frac{-2 - 1}{2 - 10}=\frac{-3}{-8}=\frac{3}{8}>0)

Answer:

A. ((2,6)), C. ((-4,7)), D. ((11,0))