Nate T. answered • 3d

Electrical Engineer with Experience Tutoring Math and Physics

Vertical asymptotes occur when the denominator is equal to zero. So, you'll want your denominator to be (x-4)*(x+6), because x=4 and x=-6 cause that to become zero.

X-intercepts happen when the numerator is equal to zero. So, you'll want your numerator to be (x+5)*(x-3), because x=-5 and x = 3 cause that to be zero.

So far we have Y = ((x+5)*(x-3)) / ((x-4)*(x+6))

Lastly, the Y-intercept is when X = 0. So, plug x=0 into your equation:

5*(-3) / (-4)*6 = -15/-24 = 5/8

So right now, the Y-intercept is 5/8. To get the y-intercept up to 7, we have to multiply the whole thing by 8/5*7

we multiply by 8/5 to get the y-intercept to 1, then multiply by 7 to get the y-intercept up to 7.

8/5* 7 = 42/5

So our new equation is:

**Y = (42/5*(x+5)*(x-3)) / ((x-4)*(x+6))**

or

**Y = (42*(x+5)*(x-3)) / (5*(x-4)*(x+6))**

you can bring the 5 to the denominator if it makes things cleaner for you. If that doesn't make sense, please let me know!