Question

Find the distance between the x and y intercept
6x-3y=-9

Answer 1

3.35

Explanation:

First find the intercepts, which you probably know means where the line crosses the x and y axes.

It crosses the x-axis when y=0, so set y equal to 0 in the equation and solve for x:

6x - 3(0) = -9

6x = -9

x = -1.5

That's where the line crosses the x-axis, at the point (-1.5,0).

Now find where it crosses the y-axis by setting x to 0:

6(0) - 3y = -9

-3y = -9

y = 3

So the y-intercept is (0,3).

Take a look now at the graph I attached. Do you see how the line is the hypotenuse of a right triangle that has one side 1.5 units long along the x-axis, and the other side 3 units long along the y-axis?

Do you remember the Pythagorean theorem? Even if you don't remember the name of it, always remember this:

`a^(2) + b^(2) = c^(2)`

If a and b are the short sides of a right triangle, then c is the hypotenuse, and that equation will always work.

We know a and b, they're 1.5 and 3, so solve for c:

c =
`\sqrt{a^(2) + b^(2)}`

c =
`\sqrt{1.5^(2) + 3^(2)` =
`√(2.25 + 9)` =
`√(11.25) = 3.35`

They'll probably want you to use "The Distance Formula," but it's the same thing, it derives from the right triangle equation. Look at it if you want: it wants you to do x₂ - x₁ and square it, then do the same for y, then add those together, and then take the square root. It's all the same steps, because it's based on the Pythagorean theorem.

Always remember
`a^(2) + b^(2) = c^(2)` and you'll never have to bother to remember the Distance Formula again, because you'll understand WHY you take the squares of the two distances, add them, then take the square root of that.