Answer: Vertex \(\left(\frac75,0\right)\), y-intercept \((0,7)\); \(x=\frac45\) or \(x=2\).

For \(y=|5x-7|\), the graph is V-shaped.

The vertex occurs when

\(5x-7=0,\)

so

\(x=\frac75.\)

Thus the vertex is

\(\left(\frac75,0\right).\)

The y-intercept is found by putting \(x=0\):

\(y=|-7|=7.\)

So the graph meets the y-axis at \((0,7)\).

For part (b),

\(5|5x-7|-1=14.\)

Hence

\(5|5x-7|=15,\)

so

\(|5x-7|=3.\)

Therefore

\(5x-7=3\quad\text{or}\quad 5x-7=-3.\)

This gives

\(x=2\quad\text{or}\quad x=\frac45.\)

So the solutions are

\(\boxed{x=\frac45\text{ or }x=2}.\)