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

Question

What equation in slope intercept form represents the line that passes through the two points?

(2, 5), (9, 2)

 

A.
y = 3/7x -41/7

B.
y = -7/3x -41/7

C.
y = 7/3x +41/7

D.
y = -3/7x + 41/7

Answer 1

The slope m=(2-5)/(9-2)= -3/7.  So the answer has to be D.

Answer 2

slope= rise/run or y/x

 

slope = (y₂-y₁)/ (x₂-x₁)

        = (2-5)/(9-2)

        = -3/7

slope intercept equation: y= mx+b

slope you found: y=-3/7x+b

this eliminates A, B, and C since the only answer that has a slope of -3/7 is D. if you want to solve for b, take one of the points and plug it into the equation you found.

 

 I use (2,5).

5= (-3/7) * 2 +b

5= (-6/7) +b

5+ 6/7=b

41/7=b

 

so plug everything in.

 

y=-3/7x+ 41/7 which gives you D