Answer:
B.y – 2 = 2(x – 5)
C.y = 2x – 8
D.y + 16 = 2(x + 4)
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-36-------------------slope 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=-26-------incorrect
Equation A is incorrect
In B
y-2=2(x-5)
y-2=2x-10
y=2x-8----------------------slope is 2
Applying the points in the equation
Point (-4,-16)
-16=2(-4)-8
-16=-8-8
-16=-16---------correct
Point (5,2)
2=2(5)-8
2=10-8
2=2----------------correct option
Equation B is correct
In C
y=2x-8-----------------------slope is 2
Applying points (-4,-16) in the equation
-16=2(-4)-8
-16=-8-8
-16=-16--------correct
Applying point (5,2)
2=2(5)-8
2=10-8
2=2-------correct
Equation C is correct
In D
y+16=2x+8
y=2x-8--------------------slope of 2
Apply the point (-4,-16) to the equation
-16=2(-4)-8
-16=-8-8
-16=-16----------correct
Apply the point (5,2)
2=2(5)-8
2=10-8
2=2------------correct
Equation D is correct