Question

What is the standard form equation of the line shown below?

Answer 1

Answer:

x - 2y + 1 = 0

Step-by-step 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