Question

Which equation is a point slope form equation for line AB ?

Answer 1

Step 1

Find the equation of the line AB

we know that

the equation of the line into point-slope form is equal to

$y-y1=m(x-x1)$

Let

$A( -2,6)\\B(2,-2)$

Find the slope m

we know that

the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute

$m=\frac{(-2-6)}{(2+2)}$

$m=\frac{(-8)}{(4)}$

$m=-2$

with the slope m and point A find the equation of the line AB

$y-6=-2(x+2)$

or

with the slope m and point B find the equation of the line AB

$y+2=-2(x-2)$

we will proceed to verify each case to determine the solution of the problem

Step 2

Verify case A

Case A) $y-2=-2(x+6)$

the slope of the line is $m=-2$

but the point $(-6,2)$ -----> not lie on the line AB (see the graph)

therefore

the case A is not the solution

Step 3

Verify case B

Case B) $y-6=-2(x+2)$

the slope of the line is $m=-2$

and the point $(-2,6)$ -----> is the point A

therefore

the case B is a solution

Step 4

Verify case C

Case C) $y-2=-2(x+2)$

the slope of the line is $m=-2$

but the point $(-2,2)$ -----> not lie on the line AB (see the graph)

therefore

the case C is not the solution

Step 5

Verify case D

Case D) $y-2=2(x+2)$

the slope of the line is $m=2$ -----> the slope is not equal to the slope AB

and the point $(-2,2)$ -----> not lie on the line AB (see the graph)

therefore

the case D is not the solution

the answer is

The equation $y-6=-2(x+2)$ is a point-slope form of the line AB

Answer 2

Answer:

AB line

Step-by-step explanation: