What is an equation for the linear function whose graph contains the points (2, 5) and (3, 0)?
enter your answers in the boxes.
y - __ = __ (x - 2)

y - 5  = (-5)(x -2) is the required line equation.

The first blank = 5

Second blank = (-5)

Step-by-step explanation:

Here, the two points are given as A(2,5) and B (3,0).

SLOPE of a line with points (a,b) and (c,d) is given as

Now, here the Slope of line AB is given as  

or, the slope of line AB = -5

by POINT SLOPE FORMULA:

The equation of line with point (x0,y0) and slope m is given as

y - y0 = m (x -x0)

So, here the point (2,5) and slope (-5), the equation of line is given as:

y - 5  = (-5)(x -2)

Now, comparing the above line equation with :  y - __ = __ (x - 2)

We get :  The first blank = (5)

                Second blank = (-5)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

step-by-step explanation:

try remembering the steps