The real zeros of a function are when the function touches or crosses the x-axis. In terms of the following linear functions, the real zeros will be the value of x when y = 0. So we simply set each equation equal to zero and solve for the x-values.
1.) y = -5x - 7
0 = -5x - 7
5x = -7
x = -7/5
The real zero is at point (-7/5, 0) and is therefore option d) -7/5.
2.) y = -7x + 3
0 = -7x + 3
7x = 3
x = 3/7
The real zero is at point (3/7, 0) and is option b.) 3/7.
3.) y = -7x + 8
0 = -7x + 8
7x = 8
x = 8/7
The real zero is at point (8/7, 0) and is option a.) 8/7.
4.) y = 3x + 1
0 = 3x + 1
-3x = 1
x = -1/3
The real zero is at point (-1/3, 0) and is option b.) -1/3.