Apoint m on a segment with endpoints x(1,-2) and y(10,3) paritions the segment in a 4: 1 ratio. find m. you must show all work to recieve credit.

M(8.2, 2)
To find a point which makes a line into 4:1 ratio, you need to divide the line into 4+1= 5 segments. You can divide the x-length and y-length of the line separately by subtracting the Y coordinate with X coordinate.

x-length= 10 -1= 9
y-length= 3- (-2)= 5

Mx= Xx coordinate + (4/5 * x-length)
Mx= 1 + (4/5 *9)= 1 + 36/5 = 8.2

My= Xy coordinate + (4/5 * y-length)
My= -2 + (4/5 * 5)= -2 + 4= 2

M (Mx,My)= M(8.2, 2)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.