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

To find the equation of a line through two points, we first need to find the slope. Recall that the slope between two points is equal to the difference in their y values divided by the difference in their x values:
\[m = \Delta y / \Delta x = (3--1)/(-2-4)=4/-6=-2/3\] Now that we have the slope and a point on the line we can plug into this equation:
\[y-y_1=m(x-x_1)\]
\[y-3=-2/3 (x--2)\]
\[y-3=-2x/3 -4/3\]
\[y=-2x/3 + 5/3\] Now we just have to figure out which of our answer choices is equivalent to this one. I'll give you a hint, try multiplying both sides by 3, that will be a good start.