Answer:
x - 2y + 1 = 0
Explanation:
This line goes through the points (-3, -1) and (3, 2). Going from the first oint to the second, we see that x increases by 6 (this is the 'run') and y increases by 3 (this is the 'rise'). Thus, the slope is m = rise / run = 3/6 = 1/2.
Starting with the slope-intercept form y = mx + b, we get
y = 2 = (1/2)(3) + b, or (after multiplying all terms by 2):
4 = 3 + 2b, or 1 = 2b, or b = 1/2
Then the equation of this line is y = mx + b, or y = (1/2)x + 1/2.
We must put this into standard form. Multiplying all terms by 2 yields
2y = x + 1, or x - 2y + 1 = 0