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.