20 points!
the sum of the x- and y-intercepts of the graph of 5x+3y = k is 32 5. find the length of the line segment joining the x- and y-intercepts.
you so much!
i literally have no idea how to do this.

Sure you do.

What is the x-intercept ? It's the point where the graph crosses the x-axis.
But y=0 at every point on the x-axis !  So the x-intercept is the point where

5x + 3(0) = k
5x = k
x = 0.2 k

Similarly ... What is the y-intercept ? It's the point where the graph crosses the
y-axis. But x=0 at every point on the y-axis !  So the y-intercept is the point where

5(0) + 3y = k
3y = k
y = k/3

The sum of the x- and y-intercepts is 32.5 .
0.2k + k/3 = 32.5
Multiply each side by 5 :
k + 5k/3 = 162.5
Multiply each side by 3 :
3k + 5k = 487.5
8k = 487.5
Divide each side by 8 :
k = 60.9375

The x-intercept is (0.2k, 0) = the point (12.1875, 0) .

The y-intercept is (0, k/3) = the point (0, 20.3125) .

Those are the two points. Now it wants you to find the distance between them.
Do you remember how to find the distance between 2 points ?

Find the (difference of their x-values) and square it.
Find the (difference of their y-values) and square it.
Add the two squares together.
Take the square root of the sum.
That's the distance between the points.

(12.1875)² + (20.3125)² = the square of the distance.

If you don't get 23.688 for the distance, then check your arithmetic.