which of the following are point slope equations of the line going through (3,6) and (1,2)?

Question

A. Y-6=2 (x-3)

B. Y-2=2 (x-1)

C. Y-2= 1/2 (x-1)

D. Y-6=1/2 (x+3)

E. Y-6= 1/2 (x-3)

F. Y-2=2 (x+1)

Answer 1

which of the following are point slope equations of the line going through (3,6) and (1,2)?
A. Y-6=2 (x-3)
B. Y-2=2 (x-1)
C. Y-2= 1/2 (x-1)
D. Y-6=1/2 (x+3)
E. Y-6= 1/2 (x-3)
F. Y-2=2 (x+1)

 

The equation of the line passing through the two points should be of the form y = mx + b, where m is the slope, and b is the y-intercept. To find the slope m, use the formula:

 

m = y₂ - y₁ / x₂ - x₁

 

Plug in the values from the two points:

 

m = 2 - 6 / 1 - 3

m = -4 / -2

m = 2

 

So, the equation so far is:

 

y = 2x + b

 

To find b, plug in the values from one of the two given points. Let's use (3,6):

 

6 = 2(3) + b

6 = 6 + b

b = 0

 

The equation then, is this:

 

y = 2x + 0

 

Or simply:

 

y = 2x

 

Now, you'll need to simplify the choices to see which ones are the same as y = 2x.

 

A. Y-6=2 (x-3)

Remove parentheses: y - 6 = 2x - 6

Add 6 to both sides:   y = 2x

B. Y-2=2 (x-1)

Remove parentheses: y - 2 = 2x - 2

Add 2 to both sides:   y = 2x

C. Y-2= 1/2 (x-1)

Remove parentheses: y - 2 = 1/2x - 1/2

Add 2 to both sides:    y = 1/2x + 3/2

 

 

D. Y-6=1/2 (x+3)

Remove parentheses: y - 6 = 1/2x + 3/2

Add 6 to both sides:   y = 1/2x + 15/2

E. Y-6= 1/2 (x-3)

Remove parentheses: y - 6 = 1/2x - 3/2

Add 6 to both sides:   y = 1/2x + 9/2

F. Y-2=2 (x+1)

Remove parentheses: y - 2 = 2x + 2

Add 2 to both sides:   y = 2x + 4

 

So, choices A and B are correct.

Answer 2

Slope of line passing through (3,6) and (1,2)

 

m = (y2 - y1)/(x2-x1)

m= (2-8)/(1-3) = 2

point slope equation

 

y = mx + b

 

since line passing through 3,6 and slope is 2

 

6 = (2x3) = b

b= 0

 

point slope equation

 

y = mx

y = 2x

 

Option B is correct

 

y-2 = 2x -2

y=2x

:)