Question

PLEASE HELP?!

A line passes through the points (2,4) and (5,6) .

Select Yes or No to tell whether each equation describes this line.

(Picture provided.)

Answer 1

y - 6 = 3/2 (x + 5) no
y - 4 = 2/3 (x - 2) yes
y - 4 = 3/2 (x + 2) no
y - 6 = 2/3 (x - 5) yes
y - 6 = 2/3 (x + 5) no
y - 6 = 3/2 (x - 5) it only goes through (5, 6), so I'm assuming that would also be no?

Hope this helps!

Answer 2

The answer in the attached figure

Explanation:

we know that

The equation of the line in point-slope form is equal to

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

we have

`A(2,4)\ B(5,6)`

Step 1

Find the slope of the line m

The formula to calculate the slope is equal to

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

Substitute the values

`m=(6-4)/(5-2)`

`m=(2)/(3)`

Step 2

Find the equation of the line with point A and the slope m

we have

`m=(2)/(3)`

`A(2,4)`

Substitute the values

`y-4=(2)/(3)(x-2)`

Step 3

Find the equation of the line with point B and the slope m

we have

`m=(2)/(3)`

`B(5,6)`

Substitute the values

`y-6=(2)/(3)(x-5)`