Identify the slope and write the equation of the line .

y=-2x+5; slope is -2

Step-by-step explanation:

slope is rise/run. we can see it rises 2 and goes left one which would give us rise/run=2/-1=-2. that is our slope.

using y=mx+b to write the equation, m is slope and b is the y-int.. we can see that the y-int. is (0,5). we can plug 5 into b.

plugging b and m in we can get the equation: y=-2x+5

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: