Answer:
3x - 2y - 12 = 0
Explanation:
First, to do this, you need to put this in slope intercept form. There are a few ways to go about doing this, but this is an easy way to do so:
- Make points out of the numbers you have (remember rise over run): the x-intercept is 4, so the point must be (4,0) because you move 4 units to the right and 0 units up. Using this same process, this makes the y-coordinate (0,-6)
- Graph the points: now that you have your points, graph them starting at the origin
- Count how many vertical units in between the two points, them the number of horizontal units, then put the rise over run and simplify: when using the intercepts, it is pretty easy to do this step. Since your y values are at 0 and -6, there are 6 vertical units in between the two points. This will be the numerator of your equation. Since your x values are at 0 and 4, there are 4 horizontal units in between your points, so 4 will be your denominator. That leaves you with the fraction 6/4. Both numbers are divisible by 2, so it can be reduced down to 3/2 as your slope.
- Put the equation together: you now know the y-intercept and slope of the equation, so you can put it together in the form y = mx + b, giving you an equation of y = 3/2x - 6.
Now you have the slope intercept form of the equation, but you are really looking for the general form:
- Move the y over so that all terms are on one side: subtract the y onto the other side to get 0 = 3/2x - y - 6
- Multiply by any denominators to get rid of fractions: since there is a fraction in this equation, 3/2, multiply all terms by 2. This gives you the equation 0 = 3x - 2y - 6.
There is nothing else left to simplify, so that is your final answer.