Find the distance between the x-intercept and the y-intercept of the graph of the equation 5x - 12y = 60.

The x-intercept of a graph is when y is 0.

5x - 12(0) = 60
x = 12
So our point is (12, 0).

Likewise, the y-intercept is when x is 0.
5(0) - 12y = 60
y = -5
So our point is (0, -5).

The distance between two points is given by the formula:
Dist = sqrt{(x0 - x1)^2 + (y0 - y1)^2}.

For this case, this is 13.

(Note that these points also form a right triangle, so you could solve for distance that way.)

Sometimes it helps to use the intercept form of a line.

5x - 12y = 60
x/12 + y/-5 = 1

The intercepts are 12 and -5, you you have a 5-12-13 right triangle.

To find the x-intercept, we set y = 0 and solve for x.

5x - 12(0) = 60
5x = 60
x = 60/5
x = 12

Therefore, the x-intercept is x = 12.

To find the y-intercept, we set x = 0 and solve for y.

5(0) - 12y = 60
-12y = 60
y = 60/-12
y = -5

Therefore, the y-intercept is y = -5.

Now, let's find the distance between the x-intercept (12, 0) and the y-intercept (0, -5) using the distance formula.

The distance formula is given by: d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates of the intercepts:
d = √((0 - 12)^2 + (-5 - 0)^2)
d = √((-12)^2 + (-5)^2)
d = √(144 + 25)
d = √169
d = 13

Therefore, the distance between the x-intercept and the y-intercept of the graph of the equation 5x - 12y = 60 is 13 units.

To find the distance between the x-intercept and the y-intercept of the graph, we need to find the coordinates of both intercepts first.

Let's start by finding the x-intercept. The x-intercept occurs when y = 0. To find the value of x, we substitute y = 0 into the equation:

5x - 12(0) = 60

This simplifies to:

5x = 60

To isolate x, divide both sides of the equation by 5:

x = 60/5

Simplifying, we get:

x = 12

So, the x-intercept is (12, 0).

Next, let's find the y-intercept. The y-intercept occurs when x = 0. To find the value of y, we substitute x = 0 into the equation:

5(0) - 12y = 60

This simplifies to:

-12y = 60

Divide both sides of the equation by -12:

y = 60/(-12)

Simplifying, we get:

y = -5

So, the y-intercept is (0, -5).

Now that we have the coordinates of both intercepts, we can find the distance between them using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's substitute the values:

Distance = sqrt((0 - 12)^2 + (-5 - 0)^2)

Simplifying, we get:

Distance = sqrt((-12)^2 + (-5)^2)
Distance = sqrt(144 + 25)
Distance = sqrt(169)
Distance = 13

Therefore, the distance between the x-intercept and the y-intercept of the graph of the equation 5x - 12y = 60 is 13 units.