Write the equation using the table and graph pictured above
(Hint: this is a 2 step equation )

y = -2x + 12

Step-by-step explanation:

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

I will use the first point (1, 10) and the last point (5, 2)

Plug in these values:

(2 - 10) / (5 - 1)

Simplify the parentheses.

= (-8) / (4)

Simplify the fraction.

-8/4

= -2

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = -2x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the last point (5, 2). Plug in the x and y values into the x and y of the standard equation.

2 = -2(5) + b

To find b, multiply the slope and the input of x(5)

2 = -10 + b

Now, add 10 to both sides to isolate b.

12 = b

Plug this into your standard equation.

y = -2x + 12

This is your equation.

Check this by plugging in the other point you have not checked yet (1, 10).

y = -2x + 12

10 = -2(1) + 12

10 = -2 + 12

10 = 10

Your equation is correct.

Hope this helps!

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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