What is the general form of the equation for a line whose x-intercept is 4 and y-intercept is -6

3x - 2y - 12 = 0

Step-by-step 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 originCount 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 - 6Multiply 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.