Prove the following statement: if the x- and y-intercepts of a line are identical nonzero numbers, the line must have a slope of-1.

We have some line with an their x- and y-intercepts the same thing.to prove that this line has a slope of -1, we need to be very general with our steps. if we only use certain values, that is only verification for those specific  values. we want to prove that this works for  all values that are nonzero.we can let n be the identical  x- and y-intercept value of this line (where n≠0)the x-intercept of a line is where the graph crosses the x-axis.the x-axis is at y = 0. therefore, this graph has the x-intercept point    (n, 0)on its graph.  the y-intercept of a line is where the graph crosses the y-axis.the y-axis is at x = 0. therefore, this graph has the y-intercept  point    (0, n)on its graph.  we know that the two points (n, 0) and (0, n) must be on this graph.we calculate the slope of this line using these two points.    (a nonzero number divided by itself is just 1.)(a positive divided by a negative results in an overall negative answer.)as we can see, we end up with a slope of -1, no matter what that nonzero value of n is.