What are the intercepts of 3x - 5y^2 = 6?

1 Answer
Apr 15, 2018

**x intercept: (2, 0)

y intercept: NONE**

Explanation:

Before we find the x intercept, let's first make x by itself:
3x - 5y^2 = 6

Add 5y^2 to both sides of the equation:
3x = 6 + 5y^2

Divide both sides by 3:
x = (6+5y^2)/3

x = 2 + (5y^2)/3

To find the x intercept, we plug in 0 for y, and solve for x:
x = 2 + (5(0)^2)/3

x = 2 + 0/3

x = 2 + 0

x = 2

So we know that the x intercept is (2, 0).


Now let's make y by itself to find the y intercept:
3x - 5y^2 = 6

Subtract 3x from both sides of the equation:
-5y^2 = 6 - 3x

Divide both sides by -5:
y^2 = (6-3x)/-5

Square root both sides:
y = +-sqrt((6-3x)/-5)

Now plug in 0 for x:
y = +-sqrt((6-3(0))/-5

y = +-sqrt(-6/5)

Since you can't square root a negative number, that means the solution is imaginary, meaning that there is no y intercept.

To check that our intercepts are correct, we can graph this:enter image source here

As you can see from the graph, it never touches the y axis, meaning that there is no value of y when x is zero. Also, you can see that the x intersect is in fact (2, 0).

Hope this helps!