Examine the following graph of a line. Which equation correctly represents the line in slope-intercept form?

y=−2/5x−2

y=−5/2x−2

y=−2x−5/2

y=−2x+5/2

y=5/2x+2

y=5/2x−2

y=-5/2-2

Step-by-step explanation:

y-intercept is -2,slope is -

y=-mx-2 (the first or second one)

then slope =(y1-y2)/(x1-x2)

slope=(3-(-2))/((-2)-0)

slope=-5/2

y=-5/2-2

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: