Question

what equation in slope intercept form represents the line that passes through the two points? (2,5),(9,2)

Answer 1

Comment
Find the slope and then use one of the points for the y intercept.
$\text {the Slope = } \dfrac{y2 - y1}{x2 - x2}$

Step One 
Find the slope
y2 = 5
y1 = 2
x2 = 2
x1 = 9
 
$\text {the Slope = } \dfrac{5 - 2}{2 - 9}$
Slope = 3/-7 I'll leave it that way for now.

Step Two
Find the y intercept

What we have so far is
y = 3/-7 x + b
Use (5,2) to solve for b
y = 2
x = 5

2 = 3*5/-7 + b
2 = 15/-7 + b      Add -15/7 to both sides.
2 + 15/7 = b
b = 2 + 2 1/7
b = 4 1/7
b = 29/7

Answer 
y = 3/-7 * x + 29/7

If you have choices, it would be a good idea to list them.

Answer 2

Answer:

The equation of the line is y = -3/7x + 41/7

Step-by-step explanation:

To find the equation of this line, you first need to find the slope. You can do this using the slope equation with the two given points.

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

m = (2 - 5)/(9 - 2)

m = -3/7

Now that we have that, we can use it along with either point in point-slope form. Start with the base form and input it.

y - y1 = m(x - x1)

y - 5 = -3/7(x - 2)

y - 5 = -3/7x + 6/7

y = -3/7x + 41/7