Select the three equationsthat pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)

B.y – 2 = 2(x – 5)

C.y = 2x – 8

D.y + 16 = 2(x + 4)

Step-by-step explanation:

An equation that passes through the points will have a gradient that is equal to that in the equation formed using the points and it will be TRUE for the values of (x,y) in the points when tested.

Finding slope obtained from the points (-4,-16) and (5,2)

m=slope=Δy/Δx

m=Δy=(2--16)/(5--4)

m=18/9= 2

Checking in the equations to identify the ones with a slope of 2 and test with the points to see if the equation holds

Rewrite the equations in the slope intercept form where y=mx+c and m is slope

In A.

y+4=2(x-16)

y+4=2x-32

y=2x-36slope is 2

⇒use points in equation to see if the equation is TRUE.

⇒Applying point (-4,-16) to the equation

-16=2(-4)-36

-16=-8-36

-16=-44 incorrect

⇒Applying point (5,2) in the equation

2=2(5)-36

2=10-36

2=-26incorrect

Equation A is incorrect

In B

y-2=2(x-5)

y-2=2x-10

y=2x-8slope is 2

Applying the points in the equation

Point (-4,-16)

-16=2(-4)-8

-16=-8-8

-16=-16correct

Point (5,2)

2=2(5)-8

2=10-8

2=2correct option

Equation B is correct

In C

y=2x-8slope is 2

Applying points (-4,-16) in the equation

-16=2(-4)-8

-16=-8-8

-16=-16correct

Applying point (5,2)

2=2(5)-8

2=10-8

2=2correct

Equation C is correct

In D

y+16=2x+8

y=2x-8slope of 2

Apply the point (-4,-16) to the equation

-16=2(-4)-8

-16=-8-8

-16=-16correct

Apply the point (5,2)

2=2(5)-8

2=10-8

2=2correct

Equation D is correct

y=x+9

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step-by-step explanation:

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: