Question

What is the equation of the line that passes through (4,-1) and (-2,3)
A. 2x-3y-5=0
B. 2x+3y-5=0
C. -2x+3y-5=0

Answer 1

Answer:

B

Step-by-step explanation:

Since this is multiple choice, we don't need to work out the equation of the line.  It will be enough to check which of these lines go through the given points.

Let's check the line given by 2x - 3y - 5 = 0.  If the point (4, -1) is on this line, then its coordinates would have to satisfy the equation.  So put in x = 4 and y = -1 to check, and we see that 2x - 3y - 5 = 2(4) - 3(-1) - 5 = 8 + 3 - 5 ≠ 0.  That didn't give zero, so the coordinates of this point don't satisfy the equation, so the point is not on the line.

Let check the line given by 2x + 3y - 5 = 0.  Again, for the point (4, -1), we have 2x + 3y - 5 = 2(4) + 3(-1) - 5 = 8 - 3 - 5 = 0.  So the line does pass through this point!  Does it also pass through the other point?  It's coordinates are (-2, 3), so we put x = -2 and y = 3.  This give 2x + 3y - 5 = 2(-2) + 3(-3) - 5 = -4 + 9 - 5 = 0.  Great!  This line passes through both points so this is the answer.

(You could also check the third line to be sure, but we're confident here.)