Question

Which is an equation of the line that goes through the points ( 4, 1) and

( 2, 3)?
A. y = 2x – 9
B. y = 2x + 7
C. y = x – 5
D. y = x + 3

Note- please explain how you got answer

Answer 1

none of the above

Explanation:

You can try the points in the equations (none works in any equation), or you can plot the points and lines (see attached). You will not find any of the offered answer choices goes through the given points.

___

You can start with the 2-point form of the equation of a line. For points (x1, y1) and (x2, y2) that equation is ...

y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

Filling in the given points, we get ...

y = (3 -1)/(2 -4)·(x -4) +1

y = 2/(-2)(x -4) +1 . . . . . simplify a bit

y = -x +4 +1 . . . . . . . . . simplify more

y = -x +5 . . . . . . . . . . . slope-intercept form